Wikipedia:WikiProject Mathematics/PlanetMath Exchange/03-XX Mathematical logic and foundations

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03-XX Mathematical logic and foundations.

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A	adequately covered
C	copied
M	merged
NC	needs copying
NM	needs merging

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Contents 1 03-00 General reference works (handbooks, dictionaries, bibliographies, etc.) 2 03A05 Philosophical and critical 3 03B05 Classical propositional logic 4 03B10 Classical first-order logic 5 03B15 Higher-order logic and type theory 6 03B22 Abstract deductive systems 7 03B35 Mechanization of proofs and logical operations 8 03B40 Combinatory logic and lambda-calculus 9 03B48 Probability and inductive logic 10 03B50 Many-valued logic 11 03B53 Logics admitting inconsistency (paraconsistent logics, discussive logics, etc.) 12 03B60 Other nonclassical logic 13 03B65 Logic of natural languages 14 03B70 Logic in computer science 15 03B99 Miscellaneous 16 03Bxx General logic 17 03C05 Equational classes, universal algebra 18 03C07 Basic properties of first-order languages and structures 19 03C10 Quantifier elimination, model completeness and related topics 20 03C15 Denumerable structures 21 03C30 Other model constructions 22 03C35 Categoricity and completeness of theories 23 03C45 Classification theory, stability and related concepts 24 03C50 Models with special properties (saturated, rigid, etc.) 25 03C52 Properties of classes of models 26 03C57 Effective and recursion-theoretic model theory 27 03C64 Model theory of ordered structures; o-minimality 28 03C68 Other classical first-order model theory 29 03C80 Logic with extra quantifiers and operators 30 03C90 Nonclassical models (Boolean-valued, sheaf, etc.) 31 03C95 Abstract model theory 32 03C99 Miscellaneous 33 03Cxx Model theory 34 03D05 Automata and formal grammars in connection with logical questions 35 03D10 Turing machines and related notions 36 03D20 Recursive functions and relations, subrecursive hierarchies 37 03D25 Recursively (computably) enumerable sets and degrees 38 03D40 Word problems, etc. 39 03D75 Abstract and axiomatic computability and recursion theory 40 03D80 Applications of computability and recursion theory 41 03Dxx Computability and recursion theory 42 03E02 Partition relations 43 03E04 Ordered sets and their cofinalities; pcf theory 44 03E05 Other combinatorial set theory 45 03E10 Ordinal and cardinal numbers 46 03E15 Descriptive set theory 47 03E17 Cardinal characteristics of the continuum 48 03E20 Other classical set theory (including functions, relations, and set algebra) 49 03E25 Axiom of choice and related propositions 50 03E30 Axiomatics of classical set theory and its fragments 51 03E35 Consistency and independence results 52 03E40 Other aspects of forcing and Boolean-valued models 53 03E45 Inner models, including constructibility, ordinal definability, and core models 54 03E50 Continuum hypothesis and Martin's axiom 55 03E55 Large cardinals 56 03E65 Other hypotheses and axioms 57 03E70 Nonclassical and second-order set theories 58 03E72 Fuzzy set theory 59 03E75 Applications of set theory 60 03E99 Miscellaneous 61 03Exx Set theory 62 03F03 Proof theory, general 63 03F07 Structure of proofs 64 03F15 Recursive ordinals and ordinal notations 65 03F20 Complexity of proofs 66 03F30 First-order arithmetic and fragments 67 03F35 Second- and higher-order arithmetic and fragments 68 03F55 Intuitionistic mathematics 69 03F60 Constructive and recursive analysis 70 03Fxx Proof theory and constructive mathematics 71 03G05 Boolean algebras 72 03G10 Lattices and related structures 73 03G12 Quantum logic 74 03G20 Lukasiewicz and Post algebras 75 03G25 Other algebras related to logic 76 03G30 Categorical logic, topoi 77 03G99 Miscellaneous 78 03Gxx Algebraic logic 79 03H05 Nonstandard models in mathematics 80 03Hxx Nonstandard models

[edit] 03-00 General reference works (handbooks, dictionaries, bibliographies, etc.)

Needs to be reviewed: 2. Paul August ☎ 20:04, 27 May 2006 (UTC)

• PM: \Psi is surjective if and only if \Psi^\ast is injective, id=6170 -- WP guess: \Psi is surjective if and only if \Psi^\ast is injective -- Status:

• PM: biconditional, id=484 -- WP: logical biconditional -- Status: M

Copied the section "Colloquial Usage" from PM into WP article. Paul August ☎ 20:37, Feb 4, 2005 (UTC)

• PM: bijection, id=425 -- WP: bijection -- Status: A

Paul August ☎ 15:03, Feb 2, 2005 (UTC)

• PM: Burali-Forti paradox, id=3484 -- WP: Burali-Forti paradox -- Status: A

Paul August ☎ 15:22, Feb 2, 2005 (UTC)

• PM: Cantor's paradox, id=3488 -- WP: Cantor's Theorem -- Status: A

Actually the PM article is misnamed, it is really about "Cantor's Theorem". WP does not have an article about "Cantor's Paradox" but should. Paul August ☎ 02:21, Feb 3, 2005 (UTC)

• PM: cartesian product, id=359 -- WP: cartesian product -- Status: A

Paul August ☎ 02:25, Feb 3, 2005 (UTC)

• PM: chain, id=1344 -- WP: chain (mathematics) -- Status: A

Paul August ☎ 02:43, Feb 3, 2005 (UTC)

• PM: characteristic function, id=350 -- WP: indicator function -- Status: M

Paul August ☎ 03:35, 10 October 2005 (UTC)

• PM: concentric circles, id=3277 -- WP: concentric -- Status: A

Paul August ☎ 03:08, Feb 3, 2005 (UTC)

• PM: conjunction, id=533 -- WP: logical conjunction -- Status: A

Paul August ☎ 03:15, Feb 3, 2005 (UTC)

• PM: cycle, id=2262 -- WP: cycle (mathematics) -- Status: C

Paul August ☎ 21:27, August 25, 2005 (UTC)

• PM: disjoint, id=604 -- WP: disjoint -- Status: A

Paul August ☎ 00:08, Feb 4, 2005 (UTC)

• PM: empty set, id=382 -- WP: empty set -- Status: A

Paul August ☎ 00:10, Feb 4, 2005 (UTC)

• PM: even number, id=4703 -- WP: even number -- Status: A

Paul August ☎ 00:22, Feb 4, 2005 (UTC)

• PM: fixed point, id=2777 -- WP: fixed point (mathematics) -- Status: A

Paul August ☎ 00:22, Feb 4, 2005 (UTC)

• PM: infinite, id=881 -- WP: infinite -- Status: A

Paul August ☎ 03:49, Feb 4, 2005 (UTC)

• PM: injective function, id=429 -- WP: injective function -- Status: A

Paul August ☎ 03:49, Feb 4, 2005 (UTC)

• PM: integer, id=403 -- WP: integer -- Status: A

PM article gives a definition of the integers as an equivalence class on NxN. Also conntains some additional algebraic properties: integral domain, ordered ring, valuation. Paul August ☎ 03:49, Feb 4, 2005 (UTC)

I would say this should go in a separate article, called say construction of integers. This in order to keep the integer page elementary. We will discuss this more. Oleg Alexandrov | talk 20:36, 5 Feb 2005 (UTC)

Well I've gone ahead and done the merging, including the bit on the construction from the natural numbers. If someone (Oleg?) wants to move this to its own article be my guest ;-) Paul August ☎ 20:38, 5 May 2006 (UTC)

• PM: inverse function, id=4645 -- WP: inverse function -- Status: M

Merged. Paul August ☎ 21:14, 5 May 2006 (UTC)

• PM: line segment, id=5783 -- WP: line segment -- Status: C

Paul August ☎ 22:17, 5 May 2006 (UTC)

• PM: linearly ordered, id=1345 -- WP: total order -- Status: A

Paul August ☎ 04:16, Feb 4, 2005 (UTC)

• PM: operator, id=1982 -- WP: operator -- Status: A

Paul August ☎ 04:32, Feb 4, 2005 (UTC)

• PM: ordered pair, id=358 -- WP: ordered pair -- Status: A

Paul August ☎ 04:32, Feb 4, 2005 (UTC)

• PM: ordered tuplet, id=6617 -- WP: n-tuple -- Status: A

Paul August ☎ 01:13, 6 May 2006 (UTC)

• PM: ordering relation, id=444 -- WP: total order -- Status: A

Paul August ☎ 20:37, Feb 4, 2005 (UTC)

• PM: partition, id=362 -- WP: partition of a set -- Status: A

Paul August ☎ 20:57, Feb 4, 2005 (UTC)

• PM: permutation, id=434 -- WP: permutation -- Status: A

Paul August ☎ 04:27, Feb 16, 2005 (UTC)

• PM: pullback, id=4569 -- WP: none -- Status: N

I don't think we need this article. It seems really to be an article about function composition. I've never heard the term "pullback" used in this context. Paul August ☎ 15:28, 5 May 2006 (UTC)

• PM: Russell's paradox, id=316 -- WP: Russell's paradox -- Status: A

Paul August ☎ 22:51, Feb 4, 2005 (UTC)

• PM: set closed under an operation, id=4562 -- WP: closure (mathematics) -- Status: A

Paul August ☎ 15:38, 5 May 2006 (UTC)

• PM: signature of a permutation, id=4061 -- WP: even and odd permutations -- Status:

The PM article contains a proposition and proof about the "signature of a permutation" which me may or may not want to include. Paul August ☎ 21:07, Feb 5, 2005 (UTC)

• PM: simple function, id=2022 -- WP: simple function -- Status: A

Paul August ☎ 04:06, 10 October 2005 (UTC)

• PM: subset, id=472 -- WP: subset -- Status: A

Paul August ☎ 03:58, Feb 5, 2005 (UTC)

• PM: surjective, id=2791 -- WP: surjective -- Status: A

Paul August ☎ 03:58, Feb 5, 2005 (UTC)

• PM: transposition, id=2274 -- WP: Transposition (mathematics) -- Status: C

Paul August ☎ 00:32, August 26, 2005 (UTC)

• PM: truth table, id=532 -- WP: truth table -- Status: A

Paul August ☎ 03:58, Feb 5, 2005 (UTC)

• PM: a surjection between finite sets of the same cardinality is bijective, id=7222 -- WP: bijection -- Status: A

Paul August ☎ 01:38, 6 May 2006 (UTC)

• PM: an injection between two finite sets of the same cardinality is bijective, id=6923 -- WP: bijection -- Status: A

Paul August ☎ 01:38, 6 May 2006 (UTC)

• PM: definition of onto linear transformation, id=7270 -- WP: linear transformation -- Status: A

Paul August ☎ 20:02, 27 May 2006 (UTC)

• PM: pointwise, id=7260 -- WP: pointwise -- Status: C

Paul August ☎ 18:25, 3 May 2006 (UTC)

• PM: (a,b)=(c,d) if and only if a=c and b=d, id=8320^new! -- WP guess: (a,b)=(c,d) if and only if a=c and b=d -- Status:

• PM: characterization of signature of a permutation, id=9621^new! -- WP guess: characterization of signature of a permutation -- Status:

• PM: endpoint, id=8165^new! -- WP guess: endpoint -- Status:

• PM: every permutation has a cycle decomposition, id=9045^new! -- WP guess: every permutation has a cycle decomposition -- Status:

• PM: example of an operator, id=7808^new! -- WP guess: example of an operator -- Status:

• PM: example of bijection, id=8680^new! -- WP guess: example of bijection -- Status:

• PM: fix, id=8277^new! -- WP guess: fix -- Status:

• PM: partition is equivalent to an equivalence relation, id=8973^new! -- WP guess: partition is equivalent to an equivalence relation -- Status:

• PM: permutation notation, id=9842^new! -- WP guess: permutation notation -- Status:

• PM: properties of cardinal numbers, id=8218^new! -- WP guess: properties of cardinal numbers -- Status:

[edit] 03A05 Philosophical and critical

All articles reviewed. Paul August ☎ 17:09, 7 May 2006 (UTC)

• PM: axiom, id=3088 -- WP: axiom -- Status: M

The PM article gives a better treatment for the historical development of the ideas of "axiom" and "postulate", which should be included in our article, in its own section called "Historical development". Paul August ☎ 17:09, 7 May 2006 (UTC)

I've now merged this content. Paul August ☎ 22:12, 9 May 2006 (UTC)

[edit] 03B05 Classical propositional logic

NM: 1. Paul August ☎ 20:53, 27 May 2006 (UTC)

• PM: CNF, id=5392 -- WP: Conjunctive normal form -- Status: A

PM article is essentially empty. Paul August ☎ 03:50, Feb 6, 2005 (UTC)

• PM: contrapositive, id=891 -- WP: contrapositive -- Status: A

Paul August ☎ 03:55, Feb 6, 2005 (UTC)

• PM: disjunction, id=536 -- WP: logical disjunction -- Status: A

Paul August ☎ 04:56, Feb 6, 2005 (UTC)

• PM: DNF, id=5677 -- WP: Disjunctive normal form -- Status: A

Paul August ☎ 05:01, Feb 6, 2005 (UTC)

• PM: equivalent, id=3769 -- WP: equivalent -- Status: A

The PM article is empty. Paul August ☎ 05:10, Feb 6, 2005 (UTC)

• PM: implication, id=480 -- WP: logical conditional -- Status: A

Paul August ☎ 05:28, Feb 6, 2005 (UTC)

• PM: Proof that contrapositive statement is true using logical equivalence, id=4379 -- WP: Contrapositive -- Status: A

Paul August ☎ 05:34, Feb 6, 2005 (UTC)

• PM: propositional logic, id=3475 -- WP: propositional logic -- Status: A

Rich Farmbrough, 19:45 11 January 2007 (GMT).

• PM: theory, id=3383 -- WP: Model theory -- Status: A

Paul August ☎ 21:04, 27 May 2006 (UTC)

• PM: transitive, id=1618 -- WP: transitive relation -- Status: A

Paul August ☎ 21:22, 27 May 2006 (UTC)

• PM: truth function, id=483 -- WP: truth function -- Status: M

Alba 21:54, 25 Feb 2005 (UTC)

• PM: every proposition is equivalent to a proposition in DNF, id=6853 -- WP: disjunctive normal form -- Status: A

Paul August ☎ 01:49, 6 May 2006 (UTC)

• PM: example of tautology, id=7311 -- WP: tautology (logic) -- Status: A

Paul August ☎ 23:12, 3 May 2006 (UTC)

• PM: tautology, id=7310 -- WP: tautology (logic) -- Status: A

Paul August ☎ 23:03, 3 May 2006 (UTC)

• PM: contradiction, id=8097^new! -- WP guess: contradiction -- Status:

• PM: contradictory statement, id=8608^new! -- WP guess: contradictory statement -- Status:

• PM: converse theorem, id=9554^new! -- WP guess: converse theorem -- Status:

• PM: examples of contrapositive, id=8529^new! -- WP guess: examples of contrapositive -- Status:

• PM: inference rule, id=9093^new! -- WP guess: inference rule -- Status:

• PM: inverse statement, id=9686^new! -- WP guess: inverse statement -- Status:

• PM: logical axiom, id=9240^new! -- WP guess: logical axiom -- Status:

• PM: logical connective, id=8605^new! -- WP guess: logical connective -- Status:

• PM: modus ponens, id=9092^new! -- WP guess: modus ponens -- Status:

• PM: modus tollens, id=9200^new! -- WP guess: modus tollens -- Status:

• PM: necessary and sufficient, id=8195^new! -- WP guess: necessary and sufficient -- Status:

• PM: negation, id=8619^new! -- WP guess: negation -- Status:

• PM: universal assumption, id=9515^new! -- WP guess: universal assumption -- Status:

[edit] 03B10 Classical first-order logic

NM: 4. Paul August ☎ 04:51, 6 October 2005 (UTC)

Needs to be reviewed: 25. Paul August ☎ 02:43, 28 May 2006 (UTC)

• PM: \Delta_1 bootstrapping, id=3344 -- WP guess: \Delta_1 bootstrapping -- Status:

• PM: arithmetical hierarchy, id=3272 -- WP: arithmetical hierarchy -- Status: NM

Paul August ☎ 18:33, Feb 6, 2005 (UTC)

Actually, this one needs more than a merge. Neither the WP article nor the PM article describes the arithmetical hierarchy on sets of reals, only on sets of naturals. They're pretty much the same thing from the descriptive set theoretic perspective, though not from the computability perspective. Article needs to be rewritten with the more inclusive descriptive set theory definitions, then the computability ones should be explained as consequences. --Trovatore 04:20, 6 October 2005 (UTC)

• PM: arithmetical hierarchy is a proper hierarchy, id=3273 -- WP: arithmetical hierarchy -- Status: NM

Paul August ☎ 01:50, 30 May 2006 (UTC)

• PM: atomic formula, id=3002 -- WP: Formula (mathematical logic) -- Status: A

Paul August ☎ 21:47, 27 May 2006 (UTC)

• PM: Boolean, id=543 -- WP: Boolean -- Status: A

Paul August ☎ 20:37, Feb 6, 2005 (UTC)

• PM: creating an infinite model, id=3043 -- WP guess: creating an infinite model -- Status:

• PM: criterion for consistency of sets of formulas, id=3035 -- WP guess: criterion for consistency of sets of formulas -- Status:

• PM: deductions are \Delta_1, id=3348 -- WP guess: deductions are \Delta_1 -- Status:

• PM: example of Gödel numbering, id=3345 -- WP: Gödel numbering -- Status: A

Paul August ☎ 22:00, 27 May 2006 (UTC)

• PM: example of well-founded induction, id=2990 -- WP guess: example of well-founded induction -- Status:

• PM: first order language, id=2999 -- WP: first-order language -- Status: A

Currently first-order language is a redirect to first-order logic, which contains all this content, it could perhaps have its own article. Paul August ☎ 22:37, 28 May 2006 (UTC)

• PM: first order logic, id=3379 -- WP: first-order logic -- Status: A

Paul August ☎ 03:41, 6 October 2005 (UTC)

• PM: first order theories, id=3012 -- WP guess: first-order theories -- Status:

• PM: free and bound variables, id=3008 -- WP guess: free and bound variables -- Status:

• PM: generalized quantifier, id=3377 -- WP guess: generalized quantifier -- Status:

• PM: Gödel numbering, id=3343 -- WP: Gödel numbering -- Status: NM

Paul August ☎ 21:17, Feb 16, 2005 (UTC)

• PM: Gödel's incompleteness theorems, id=4580 -- WP: Gödel's incompleteness theorems -- Status: NM

Paul August ☎ 21:36, Feb 16, 2005 (UTC)

• PM: Herbrand structure, id=6105 -- WP: Herbrand structure -- Status: C

copied by someone else. linas (talk) 22:31, 4 June 2008 (UTC)

• PM: Herbrand's theorem (first-order logic), id=6104 -- WP: Herbrand's theorem -- Status: A

Mathemens (talk) 22:16, 30 April 2008 (UTC) Someone has seemingly already covered this article. Changed status.

• PM: Lindenbaum algebra, id=2997 -- WP: Lindenbaum-Tarski algebra -- Status: A

Paul August ☎ 03:22, 6 October 2005 (UTC)

• PM: Lindström's theorem, id=4556 -- WP guess: Lindström's theorem -- Status:

• PM: logic, id=3380 -- WP guess: logic -- Status:

• PM: logical language, id=3376 -- WP guess: logical language -- Status:

• PM: Presburger arithmetic, id=3185 -- WP: Presburger arithmetic -- Status: A

Paul August ☎ 03:10, 6 October 2005 (UTC)

• PM: proof of compactness theorem for first-order logic, id=3034 -- WP guess: proof of compactness theorem for first-order logic -- Status:

• PM: proof of principle of transfinite induction, id=2704 -- WP guess: proof of principle of transfinite induction -- Status:

• PM: proof of the well-founded induction principle, id=2989 -- WP guess: proof of the well-founded induction principle -- Status:

• PM: quantifier, id=3360 -- WP guess: quantifier -- Status:

• PM: quantifier free, id=4031 -- WP guess: quantifier free -- Status:

• PM: R-minimal element, id=2998 -- WP guess: R-minimal element -- Status:

• PM: Skolemization, id=3361 -- WP guess: Skolemization -- Status:

• PM: subformula, id=3001 -- WP guess: subformula -- Status:

• PM: syntactic compactness theorem for first order logic, id=3033 -- WP guess: syntactic compactness theorem for first-order logic -- Status:

• PM: transfinite induction, id=2703 -- WP: transfinite induction -- Status: A

Paul August ☎ 03:54, Feb 13, 2005 (UTC)

• PM: universal relation, id=3342 -- WP guess: universal relation -- Status:

• PM: universal relations exist for each level of the arithmetical hierarchy, id=3349 -- WP guess: universal relations exist for each level of the arithmetical hierarchy -- Status:

• PM: well-founded induction, id=2988 -- WP: Well-founded relation -- Status: NM

Paul August ☎ 02:43, 28 May 2006 (UTC)

• PM: well-founded induction on formulas, id=3000 -- WP guess: well-founded induction on formulas -- Status:

• PM: prenex form, id=6852 -- WP: prenex normal form -- Status: A

Paul August ☎ 23:10, 3 May 2006 (UTC)

• PM: fuzzy logic, id=8746^new! -- WP guess: fuzzy logic -- Status:

[edit] 03B15 Higher-order logic and type theory

Needs to be merged: 1. Paul August ☎ 05:17, Feb 17, 2005 (UTC)

Needs to be reviewed: 4. Paul August ☎ 05:17, Feb 17, 2005 (UTC)

• PM: analytic hierarchy, id=3305 -- WP article: analytical hierarchy -- Status:

PM article has erroneous title; we have the correct one. Our article still needs work. --Trovatore 05:00, 6 October 2005 (UTC)

• PM: game-theoretical quantifier, id=3363 -- WP guess: game-theoretical quantifier -- Status:

• PM: Härtig's quantifier, id=3362 -- WP guess: Härtig's quantifier -- Status:

• PM: Russell's theory of types, id=4555 -- WP: type theory -- Status: NM

Paul August ☎ 05:17, Feb 17, 2005 (UTC)

• PM: second order logic, id=3385 -- WP guess: second-order logic -- Status:

• PM: point-free geometry, id=8747^new! -- WP guess: point-free geometry -- Status:

[edit] 03B22 Abstract deductive systems

• PM: consequence operator, id=8646^new! -- WP guess: consequence operator -- Status:

• PM: consequence operator determined by a class of subsets, id=8671^new! -- WP guess: consequence operator determined by a class of subsets -- Status:

• PM: consequence operator is determined by its fixed points, id=8672^new! -- WP guess: consequence operator is determined by its fixed points -- Status:

• PM: finiteness of C_\cup and C_{\cap}, id=8677^new! -- WP guess: finiteness of C_\cup and C_\cap -- Status:

• PM: operations on consequence operators, id=8669^new! -- WP guess: operations on consequence operators -- Status:

• PM: proof that C_\cup and C_\cap are consequence operators, id=8670^new! -- WP guess: proof that C_\cup and C_\cap are consequence operators -- Status:

• PM: superfluity of the third defining property for finite consequence operator, id=8678^new! -- WP guess: superfluity of the third defining property for finite consequence operator -- Status:

[edit] 03B35 Mechanization of proofs and logical operations

[edit] 03B40 Combinatory logic and lambda-calculus

Needs to be merged: 2. Paul August ☎ 04:50, Feb 17, 2005 (UTC)

• PM: Church integer, id=2785 -- WP: Church integer -- Status: A

Paul August ☎ 04:50, Feb 17, 2005 (UTC)

• PM: combinatory logic, id=2784 -- WP: combinatory logic -- Status: NM

Paul August ☎ 04:45, Feb 17, 2005 (UTC)

• PM: lambda calculus, id=2788 -- WP: lambda calculus -- Status: NM

Paul August ☎ 21:08, Feb 16, 2005 (UTC)

[edit] 03B48 Probability and inductive logic

Needs to be merged: 1. Paul August ☎ 04:51, Feb 17, 2005 (UTC)

• PM: conditional probability, id=2097 -- WP: conditional probability -- Status: A

Paul August ☎ 04:10, Feb 13, 2005 (UTC)

• PM: induction, id=2263 -- WP: Mathematical induction -- Status: NM

Paul August ☎ 04:04, Feb 13, 2005 (UTC)

[edit] 03B50 Many-valued logic

All articles processed. Paul August ☎ 05:10, Feb 17, 2005 (UTC)

• PM: neutrosophic logic, id=5843 -- WP: (none) -- Status: N

Apparently deleted. See also neutrosophic probability in 60A10 Probabilistic measure theory. Ben Cairns 06:10, 3 Feb 2005 (UTC).

[edit] 03B53 Logics admitting inconsistency (paraconsistent logics, discussive logics, etc.)

All articles processed. Paul August ☎ 05:11, Feb 17, 2005 (UTC)

[edit] 03B60 Other nonclassical logic

All articles processed. Paul August ☎ 05:12, Feb 17, 2005 (UTC)

[edit] 03B65 Logic of natural languages

• PM: standard enumeration, id=4158 -- WP guess: standard enumeration -- Status:

[edit] 03B70 Logic in computer science

• PM: more examples of Polish notation, id=8354^new! -- WP guess: more examples of Polish notation -- Status:

• PM: more examples of reverse Polish notation, id=8257^new! -- WP guess: more examples of reverse Polish notation -- Status:

• PM: Polish notation, id=8243^new! -- WP guess: Polish notation -- Status:

• PM: reverse Polish notation, id=8251^new! -- WP guess: reverse Polish notation -- Status:

• PM: shunting yard algorithm, id=8256^new! -- WP guess: shunting yard algorithm -- Status:

[edit] 03B99 Miscellaneous

Needs to be reviewed: 6. Paul August ☎ 03:01, 28 May 2006 (UTC)

• PM: Beth property, id=4559 -- WP guess: Beth property -- Status:

• PM: compactness, id=4557 -- WP guess: compactness -- Status:

• PM: consistent, id=3386 -- WP guess: consistent -- Status:

• PM: Hofstadter's MIU system, id=4732 -- WP: none -- Status: N

Paul August ☎ 02:58, 28 May 2006 (UTC)

• PM: IF-logic, id=4583 -- WP guess: IF-logic -- Status:

• PM: interpolation property, id=4558 -- WP guess: interpolation property -- Status:

• PM: sentence, id=3387 -- WP: sentence (mathematical logic) -- Status: A

Paul August ☎ 03:01, 28 May 2006 (UTC)

• PM: Tarski's result on the undefinability of truth, id=4552 -- WP guess: Tarski's result on the undefinability of truth -- Status:

• PM: Banach-Tarski paradox, id=4464 -- WP guess: Banach-Tarski paradox -- Status:

• PM: paradox, id=8201^new! -- WP guess: paradox -- Status:

[edit] 03Bxx General logic

[edit] 03C05 Equational classes, universal algebra

Needs to be reviewed: 6. Paul August ☎ 05:06, Feb 17, 2005 (UTC)

• PM: congruence, id=4486 -- WP guess: congruence -- Status:

• PM: every congruence is the kernel of a homomorphism, id=4541 -- WP guess: every congruence is the kernel of a homomorphism -- Status:

• PM: homomorphic image of a \Sigma-structure is a \Sigma-structure, id=4488 -- WP guess: homomorphic image of a \Sigma-structure is a \Sigma-structure -- Status:

• PM: kernel, id=4485 -- WP guess: kernel -- Status:

• PM: kernel of a homomorphism is a congruence, id=4519 -- WP guess: kernel of a homomorphism is a congruence -- Status:

• PM: quotient structure, id=4487 -- WP guess: quotient structure -- Status:

• PM: Diamond Lemma, id=7235 -- WP guess: Diamond Lemma -- Status:

• PM: equational class, id=9034^new! -- WP guess: equational class -- Status:

[edit] 03C07 Basic properties of first-order languages and structures

Needs to be reviewed: 20. Paul August ☎ 05:04, 28 May 2006 (UTC)

NM: 2. Paul August ☎ 05:04, 28 May 2006 (UTC)

• PM: alphabet, id=1681 -- WP guess: alphabet -- Status:

• PM: axiomatizable theory, id=3016 -- WP guess: axiomatizable theory -- Status:

• PM: definable, id=4012 -- WP guess: definable -- Status:

• PM: definable type, id=4064 -- WP guess: definable type -- Status:

• PM: downward Lowenheim-Skolem theorem, id=3394 -- WP:Löwenheim–Skolem theorem -- Status: NM

Paul August ☎ 05:04, 28 May 2006 (UTC)

• PM: example of definable type, id=4070 -- WP guess: example of definable type -- Status:

• PM: example of strongly minimal, id=4030 -- WP guess: example of strongly minimal -- Status:

• PM: first isomorphism theorem, id=4582 -- WP guess: first isomorphism theorem -- Status:

• PM: language, id=1767 -- WP guess: language -- Status:

• PM: length of a string, id=2708 -- WP: string (computer science) -- Status: A

in the "formal theory" section. CryptoDerk 20:18, Apr 30, 2005 (UTC)

• PM: models constructed from constants, id=3049 -- WP guess: models constructed from constants -- Status:

• PM: proof of homomorphic image of a \Sigma-structure is a \Sigma-structure, id=4489 -- WP guess: proof of homomorphic image of a \Sigma-structure is a \Sigma-structure -- Status:

• PM: relational structure, id=5733 -- WP guess: relational structure -- Status:

• PM: satisfaction relation, id=3032 -- WP guess: satisfaction relation -- Status:

• PM: signature, id=4603 -- WP guess: signature -- Status:

• PM: Stone space, id=3949 -- WP guess: Stone space -- Status:

• PM: strongly minimal, id=4019 -- WP guess: strongly minimal -- Status:

• PM: structure preserving mappings, id=3021 -- WP guess: structure preserving mappings -- Status:

• PM: structures, id=3017 -- WP guess: structures -- Status:

• PM: substring, id=2686 -- WP guess: substring -- Status:

• PM: substructure, id=4579 -- WP guess: substructure -- Status:

• PM: type, id=3913 -- WP guess: type -- Status:

• PM: upward Lowenheim-Skolem theorem, id=3393 -- WP: Löwenheim–Skolem theorem -- Status: NM

Paul August ☎ 05:04, 28 May 2006 (UTC)

• PM: theory of formal languages, id=6843 -- WP guess: theory of formal languages -- Status:

[edit] 03C10 Quantifier elimination, model completeness and related topics

All articles processed. Paul August ☎ 05:23, Feb 17, 2005 (UTC)

[edit] 03C15 Denumerable structures

Needs to be merged: 1. Paul August ☎ 05:27, Feb 17, 2005 (UTC)

• PM: random graph (infinite), id=4137 -- WP: random graph -- Status: NM

Paul August ☎ 05:27, Feb 17, 2005 (UTC)

[edit] 03C30 Other model constructions

All articles processed. Paul August ☎ 05:35, Feb 17, 2005 (UTC)

[edit] 03C35 Categoricity and completeness of theories

Needs to be merged: 2. Paul August ☎ 05:42, Feb 17, 2005 (UTC)

• PM: \kappa-categorical, id=3390 -- WP: Categorical (model theory) -- Status: A

Arthur Rubin 21:25, 22 August 2005 (UTC)

• PM: proof of Vaught's test, id=3395 -- WP: Model theory -- Status: NM

Paul August ☎ 05:42, Feb 17, 2005 (UTC)

• PM: Vaught's test, id=3391 -- WP: Model theory -- Status: NM

Paul August ☎ 05:42, Feb 17, 2005 (UTC)

• PM: countably categorical structures, id=7045 -- WP guess: countably categorical structures -- Status:

• PM: oligomorphic permutation group, id=7044 -- WP guess: oligomorphic permutation group -- Status:

[edit] 03C45 Classification theory, stability and related concepts

All articles processed. Paul August ☎ 05:43, Feb 17, 2005 (UTC)

[edit] 03C50 Models with special properties (saturated, rigid, etc.)

Needs to be reviewed: 3. Paul August ☎ 05:46, Feb 17, 2005 (UTC)

• PM: example of a universal structure, id=3925 -- WP guess: example of a universal structure -- Status:

• PM: homogeneous, id=3923 -- WP guess: homogeneous -- Status:

• PM: universal structure, id=3922 -- WP guess: universal structure -- Status:

[edit] 03C52 Properties of classes of models

Needs to be reviewed: 1. Paul August ☎ 05:47, Feb 17, 2005 (UTC)

• PM: amalgamation property, id=3964 -- WP guess: amalgamation property -- Status:

[edit] 03C57 Effective and recursion-theoretic model theory

Needs to be reviewed: 1. Paul August ☎ 05:50, Feb 17, 2005 (UTC)

• PM: automatic presentation, id=5736 -- WP guess: automatic presentation -- Status:

[edit] 03C64 Model theory of ordered structures; o-minimality

Needs to be merged: 1. Paul August ☎ 05:57, Feb 17, 2005 (UTC)

Needs to be reviewed: 2. Paul August ☎ 05:57, Feb 17, 2005 (UTC)

• PM: infinitesimal, id=3918 -- WP guess: infinitesimal -- Status:

• PM: o-minimality, id=3919 -- WP guess: o-minimality -- Status:

• PM: real closed fields, id=3920 -- WP: real closed field -- Status: NM

Paul August ☎ 02:23, Feb 14, 2005 (UTC)

[edit] 03C68 Other classical first-order model theory

Needs to be reviewed: 1. Paul August ☎ 05:58, Feb 17, 2005 (UTC)

• PM: imaginaries, id=3990 -- WP guess: imaginaries -- Status:

[edit] 03C80 Logic with extra quantifiers and operators

All articles processed. Paul August ☎ 05:58, Feb 17, 2005 (UTC)

[edit] 03C90 Nonclassical models (Boolean-valued, sheaf, etc.)

All articles processed. Paul August ☎ 05:14, 28 May 2006 (UTC)

• PM: Boolean valued model, id=3184 -- WP: Boolean-valued model -- Status: A

Paul August ☎ 05:14, 28 May 2006 (UTC)

[edit] 03C95 Abstract model theory

All articles processed. Paul August ☎ 06:00, Feb 17, 2005 (UTC)

[edit] 03C99 Miscellaneous

Needs to be merged: 5. Paul August ☎ 06:01, Feb 17, 2005 (UTC)

• PM: axiom of foundation, id=3485 -- WP: axiom of regularity -- Status: NM

Paul August ☎ 01:27, Feb 14, 2005 (UTC)

• PM: elementarily equivalent, id=3388 -- WP: elementarily equivalent -- Status: NM

A bit of notation could be merged. Paul August ☎ 01:37, Feb 14, 2005 (UTC)

• PM: elementary embedding, id=3389 -- WP: elementary embedding -- Status: NM

Paul August ☎ 01:53, Feb 14, 2005 (UTC)

• PM: model, id=3384 -- WP: model theory -- Status: NM

Or perhaps it could be copied to say: Model (model theory). Paul August ☎ 01:58, Feb 14, 2005 (UTC)

• PM: proof equivalence of formulation of foundation, id=3487 -- WP: axiom of regularity -- Status: NM

Paul August ☎ 02:00, Feb 14, 2005 (UTC)

• PM: model theory, id=8616^new! -- WP guess: model theory -- Status:

[edit] 03Cxx Model theory

[edit] 03D05 Automata and formal grammars in connection with logical questions

Needs to be merged: 1. Paul August ☎ 19:58, Feb 16, 2005 (UTC)

• PM: automaton, id=2550 -- WP: finite state machine -- Status: NM

Paul August ☎ 02:46, Feb 14, 2005 (UTC)

[edit] 03D10 Turing machines and related notions

Needs to be merged: 4. Paul August ☎ 06:02, Feb 17, 2005 (UTC)

• PM: deterministic finite automaton, id=2553 -- WP: deterministic finite state machine -- Status: NM

Paul August ☎ 02:34, Feb 14, 2005 (UTC)

• PM: non-deterministic finite automaton, id=2557 -- WP: nondeterministic finite state machine -- Status: NM

Paul August ☎ 02:39, Feb 14, 2005 (UTC)

• PM: non-deterministic pushdown automaton, id=2571 -- WP: pushdown automaton -- Status: NM

• PM: Turing computable, id=2800 -- WP: computable function -- Status: A

Paul August ☎ 03:08, Feb 14, 2005 (UTC)

• PM: Turing machine, id=3357 -- WP: Turing machine -- Status: NM

Paul August ☎ 03:01, Feb 14, 2005 (UTC)

[edit] 03D20 Recursive functions and relations, subrecursive hierarchies

Needs to be merged: 3. Paul August ☎ 06:24, Feb 17, 2005 (UTC)

• PM: alternative characterizations of recursive functions, id=6139 -- WP: recursive function -- Status: NM

Paul August ☎ 06:20, Feb 17, 2005 (UTC)

• PM: pairing function, id=6140 -- WP: pairing function -- Status: NM

Paul August ☎ 06:24, Feb 17, 2005 (UTC)

• PM: primitive recursive, id=2801 -- WP: primitive recursive -- Status: A

Paul August ☎ 06:12, Feb 17, 2005 (UTC)

• PM: recurrence relation, id=664 -- WP: recurrence relation -- Status: A

Paul August ☎ 06:18, Feb 17, 2005 (UTC)

• PM: recursive function, id=6135 -- WP: recursive function -- Status: NM

Paul August ☎ 06:24, Feb 17, 2005 (UTC)

• PM: characterization of primitive recursive functions of one variable, id=8983^new! -- WP guess: characterization of primitive recursive functions of one variable -- Status:

[edit] 03D25 Recursively (computably) enumerable sets and degrees

Needs to be merged: 2. Paul August ☎ 19:59, Feb 17, 2005 (UTC)

• PM: computable number, id=4170 -- WP: computable number -- Status: NM

Paul August ☎ 19:55, Feb 17, 2005 (UTC)

• PM: recursively enumerable, id=3045 -- WP: recursively enumerable set -- Status: NM

Paul August ☎ 19:59, Feb 17, 2005 (UTC)

[edit] 03D40 Word problems, etc.

[edit] 03D75 Abstract and axiomatic computability and recursion theory

All articles processed. Paul August ☎ 20:17, Feb 17, 2005 (UTC)

• PM: Ackermann function, id=2799 -- WP: Ackermann function -- Status: A

Paul August ☎ 20:11, Feb 17, 2005 (UTC)

• PM: halting problem, id=1622 -- WP: halting problem -- Status: A

Paul August ☎ 20:17, Feb 17, 2005 (UTC)

[edit] 03D80 Applications of computability and recursion theory

• PM: Penrose's first Gödelian argument, id=9391^new! -- WP guess: Penrose's first Gödelian argument -- Status:

• PM: Penrose's second Gödelian argument, id=9392^new! -- WP guess: Penrose's second Gödelian argument -- Status:

• PM: strong AI thesis, id=9422^new! -- WP guess: strong AI thesis -- Status:

• PM: weak AI thesis, id=9423^new! -- WP guess: weak AI thesis -- Status:

[edit] 03Dxx Computability and recursion theory

[edit] 03E02 Partition relations

All articles processed. Paul August ☎ 00:05, August 23, 2005 (UTC)

• PM: perfect ruler, id=1620 -- WP: perfect ruler -- Status: C

Rich Farmbrough 22:43, 22 August 2005 (UTC)

This is related to but different from Golomb ruler. Paul August ☎ 20:36, Feb 17, 2005 (UTC)

[edit] 03E04 Ordered sets and their cofinalities; pcf theory

Needs to be merged: 5. Paul August ☎ 04:53, Feb 18, 2005 (UTC)

• PM: another definition of cofinality, id=4626 -- WP: cofinality -- Status: NM

Paul August ☎ 20:51, Feb 17, 2005 (UTC)

• PM: cofinality, id=2205 -- WP: cofinality -- Status: NM

Paul August ☎ 20:51, Feb 17, 2005 (UTC)

• PM: maximal element, id=2749 -- WP: maximal element -- Status: NM

Paul August ☎ 20:59, Feb 17, 2005 (UTC)

• PM: minimal and maximal number, id=6118 -- WP: greatest element -- Status: NM

Paul August ☎ 04:24, Feb 18, 2005 (UTC)

• PM: partitions less than cofinality, id=3287 -- WP: cofinality -- Status: NM

Paul August ☎ 04:26, Feb 18, 2005 (UTC)

• PM: well ordered set, id=271 -- WP: well ordered -- Status: A

Paul August ☎ 04:53, Feb 18, 2005 (UTC)

• PM: visualizing maximal elements, id=7593 -- WP guess: visualizing maximal elements -- Status:

• PM: frequently in, id=9569^new! -- WP guess: frequently in -- Status:

[edit] 03E05 Other combinatorial set theory

Needs to be merged: 3. Paul August ☎ 05:09, Feb 18, 2005 (UTC)

Needs to be reviewed: 8. Paul August ☎ 05:09, Feb 18, 2005 (UTC)

• PM: antichain, id=3212 -- WP: antichain -- Status: NM

Paul August ☎ 04:57, Feb 18, 2005 (UTC)

• PM: Aronszajn tree, id=3217 -- WP guess: Aronszajn tree -- Status:

• PM: branch, id=3211 -- WP guess: branch -- Status:

• PM: Erdős-Rado theorem, id=3366 -- WP guess: Erdős-Rado theorem -- Status:

• PM: example of Aronszajn tree, id=3219 -- WP guess: example of Aronszajn tree -- Status:

• PM: example of tree (set theoretic), id=3213 -- WP guess: example of tree (set theoretic) -- Status:

• PM: pigeonhole principle, id=502 -- WP: pigeonhole principle -- Status: NM

Paul August ☎ 05:09, Feb 18, 2005 (UTC)

• PM: proof of pigeonhole principle, id=4106 -- WP: pigeonhole principle -- Status: NM

Paul August ☎ 05:09, Feb 18, 2005 (UTC)

• PM: proof that \omega has the tree property, id=3218 -- WP guess: proof that \omega has the tree property -- Status:

• PM: Suslin tree, id=3220 -- WP guess: Suslin tree -- Status:

• PM: tree (set theoretic), id=3210 -- WP guess: tree (set theoretic) -- Status:

• PM: another proof of pigeonhole principle, id=8086^new! -- WP guess: another proof of pigeonhole principle -- Status:

[edit] 03E10 Ordinal and cardinal numbers

NM: 14. Paul August ☎ 17:07, August 26, 2005 (UTC)

Needs to be reviewed: 11. Paul August ☎ 03:22, 28 May 2006 (UTC)

• PM: \kappa-complete, id=3230 -- WP guess: \kappa-complete -- Status:

• PM: additively indecomposable, id=4056 -- WP: additively indecomposable ordinal -- Status: C

Mathemens (talk) 22:32, 30 April 2008 (UTC)

• PM: aleph numbers, id=5710 -- WP: aleph number -- Status: NM

Paul August ☎ 05:32, Feb 18, 2005 (UTC)

• PM: beth numbers, id=5740 -- WP: beth number -- Status: NM

Paul August ☎ 05:32, Feb 18, 2005 (UTC)

• PM: Cantor's diagonal argument, id=2109 -- WP: Cantor's diagonal argument -- Status: NM

Paul August ☎ 15:10, Feb 18, 2005 (UTC)

• PM: Cantor's theorem, id=3051 -- WP: Cantor's theorem -- Status: A

Paul August ☎ 15:30, Feb 18, 2005 (UTC)

• PM: cardinal arithmetic, id=5701 -- WP: cardinal number -- Status: NM

Paul August ☎ 15:46, Feb 18, 2005 (UTC)

• PM: cardinal exponentiation under GCH, id=6584 -- WP: cardinal number -- Status: NM

Paul August ☎ 15:48, Feb 18, 2005 (UTC)

• PM: cardinal number, id=1302 -- WP: cardinal number -- Status: A

Paul August ☎ 15:56, Feb 18, 2005 (UTC)

• PM: cardinal successor, id=5439 -- WP: successor cardinal -- Status: A

Paul August ☎ 15:58, Feb 18, 2005 (UTC)

• PM: cardinality, id=963 -- WP: cardinality -- Status: NM

Paul August ☎ 16:07, Feb 18, 2005 (UTC)

• PM: cardinality of a countable union, id=934 -- WP: countable set -- Status: A

Paul August ☎ 16:12, Feb 18, 2005 (UTC)

• PM: cardinality of the continuum, id=5708 -- WP: cardinality of the continuum -- Status: M

Paul August ☎ 01:04, August 26, 2005 (UTC)

• PM: cardinality of the rationals, id=921 -- WP: rational number -- Status: A

Paul August ☎ 16:46, Feb 18, 2005 (UTC)

• PM: classes of ordinals and enumerating functions, id=4053 -- WP guess: classes of ordinals and enumerating functions -- Status:

• PM: club, id=3227 -- WP: club set -- Status: M

Porcher 17:06, 3 Apr 2005 (UTC)

• PM: club filter, id=3231 -- WP: club filter -- Status: C

Porcher 16:56, 3 Apr 2005 (UTC)

• PM: countable, id=880 -- WP: countable set -- Status: A

Paul August ☎ 18:32, Feb 18, 2005 (UTC)

• PM: countably infinite, id=883 -- WP: countable set -- Status: A

Paul August ☎ 22:05, Feb 19, 2005 (UTC)

• PM: finite, id=500 -- WP: finite -- Status: A

Paul August ☎ 22:07, Feb 19, 2005 (UTC)

• PM: fixed points of normal functions, id=4054 -- WP guess: fixed points of normal functions -- Status:

• PM: Fodor's lemma, id=3232 -- WP: Fodor's lemma -- Status: C

This PM article along with the PM article "Proof of Fordor's lemma" has been copied to Fodor's lemma and mildly edited. Porcher 16:55, 1 Apr 2005 (UTC)

• PM: height of an algebraic number, id=3954 -- WP guess: height of an algebraic number -- Status:

• PM: Hilbert's hotel, id=5781 -- WP: Hilbert's paradox of the Grand Hotel -- Status: A

Paul August ☎ 20:26, Feb 20, 2005 (UTC)

• PM: if A is infinite and B is a finite subset of A\,\!, then A\setminus B is infinite, id=4199 -- WP: Countable set -- Status: NM

Paul August ☎ 16:02, Mar 13, 2005 (UTC)

• PM: König's theorem, id=5598 -- WP: König's theorem -- Status: NM

The PM article has a proof of the theorem. Paul August ☎ 21:05, Feb 20, 2005 (UTC)

• PM: limit cardinal, id=5438 -- WP: limit cardinal -- Status: A

Paul August ☎ 21:12, Feb 20, 2005 (UTC)

• PM: natural number, id=387 -- WP: natural number -- Status: A

Paul August ☎ 21:20, Feb 20, 2005 (UTC)

• PM: ordinal arithmetic, id=4052 -- WP: ordinal number -- Status: NM

Paul August ☎ 03:26, Mar 13, 2005 (UTC)

• PM: ordinal number, id=1300 -- WP: ordinal number -- Status: A

Paul August ☎ 03:20, Mar 13, 2005 (UTC)

• PM: power set, id=136 -- WP: power set -- Status: NM

Paul August ☎ 03:30, Mar 13, 2005 (UTC)

• PM: proof of Cantor's theorem, id=3053 -- WP: Cantor's theorem -- Status: A

Paul August ☎ 03:34, Mar 13, 2005 (UTC)

• PM: proof of fixed points of normal functions, id=4055 -- WP guess: proof of fixed points of normal functions -- Status:

• PM: proof of Fodor's lemma, id=3234 -- WP: Fodor's lemma -- Status: C

This PM article along with the PM article "Fordor's lemma" has been copied to Fodor's lemma and mildly edited. Porcher 16:58, 1 Apr 2005 (UTC)

• PM: proof of Schroeder-Bernstein theorem, id=3156 -- WP: Cantor–Bernstein–Schroeder theorem -- Status: A

The PM proof is more detailed and could perhaps be merged. Paul August ☎ 04:03, Mar 13, 2005 (UTC)

The PM proof is actually just plain different. I added a link to the WP article, that should suffice. linas 04:42, 24 November 2006 (UTC)

• PM: proof of the existence of transcendental numbers, id=3955 -- WP guess: transcendental number -- Status: NM

Paul August ☎ 04:09, Mar 13, 2005 (UTC)

• PM: proof of theorems in additively indecomposable, id=4057 -- WP guess: proof of theorems in additively indecomposable -- Status:

• PM: proof that countable unions are countable, id=935 -- WP: Countable set -- Status: A

This proof could be merged into Countable set. Paul August ☎ 15:07, Mar 13, 2005 (UTC)

• PM: proof that the rationals are countable, id=927 -- WP guess: proof that the rationals are countable -- Status:

• PM: Schroeder-Bernstein theorem, id=2091 -- WP: Cantor–Bernstein–Schroeder theorem -- Status: A

Paul August ☎ 04:03, Mar 13, 2005 (UTC)

• PM: sequence, id=397 -- WP: sequence -- Status: NM

The PM article contains a generalization of sequence to a function whose domain is any ordinal, not just N. Paul August ☎ 20:13, Mar 13, 2005 (UTC)

• PM: stationary set, id=3228 -- WP: stationary set -- Status: A

This article has been copied prom the PM original and classified as a stub. Porcher 17:09, 1 Apr 2005 (UTC)

This article no longer uses any PM text, so I've changed the status to "A". Paul August ☎ 16:05, 21 February 2006 (UTC)

• PM: successor, id=385 -- WP guess: successor -- Status:

• PM: successor cardinal, id=5440 -- WP: successor cardinal -- Status: A

Paul August ☎ 02:45, Mar 14, 2005 (UTC)

• PM: uncountable, id=884 -- WP: uncountable set -- Status: A

Paul August ☎ 03:58, Mar 14, 2005 (UTC)

• PM: Veblen function, id=4058 -- WP guess: Veblen function -- Status:

• PM: von Neumann integer, id=2786 -- WP: Natural number -- Status: NM

The PM article uses the term "von Neumann integer", not used in WP. Paul August ☎ 03:05, Mar 14, 2005 (UTC)

• PM: von Neumann ordinal, id=2787 -- WP: ordinal -- Status: NM

The PM article uses the term "von Neumann ordinal", not used in WP. Paul August ☎ 03:05, Mar 14, 2005 (UTC)

• PM: weakly compact cardinal, id=3177 -- WP: weakly compact cardinal -- Status:

• PM: weakly compact cardinals and the tree property, id=3223 -- WP: weakly compact cardinal -- Status:

• PM: algebraic numbers are countable, id=6999 -- WP guess: algebraic numbers are countable -- Status:

• PM: all algebraic numbers in a sequence, id=7003 -- WP guess: all algebraic numbers in a sequence -- Status:

• PM: Cantor Normal Form, id=7448 -- WP guess: Cantor Normal Form -- Status:

• PM: normal (ordinal) function, id=7451 -- WP guess: normal (ordinal) function -- Status:

• PM: the cartesian product of a finite number of countable sets is countable, id=7142 -- WP guess: the cartesian product of a finite number of countable sets is countable -- Status:

• PM: another proof of cardinality of the rationals, id=8073^new! -- WP guess: another proof of cardinality of the rationals -- Status:

• PM: cardinality of disjoint union of finite sets, id=8696^new! -- WP guess: cardinality of disjoint union of finite sets -- Status:

• PM: intercession, id=9327^new! -- WP guess: intercession -- Status:

• PM: motivation for von Neumann ordinals, id=9089^new! -- WP guess: motivation for von Neumann ordinals -- Status:

• PM: open and closed intervals have the same cardinality, id=7675^new! -- WP guess: open and closed intervals have the same cardinality -- Status:

• PM: subsets of countable sets are countable, id=7721^new! -- WP guess: subsets of countable sets are countable -- Status:

• PM: the set of all real transcendental numbers is uncountable, id=8206^new! -- WP guess: the set of all real transcendental numbers is uncountable -- Status:

• PM: uniqueness of cardinality, id=8603^new! -- WP guess: uniqueness of cardinality -- Status:

[edit] 03E15 Descriptive set theory

• PM: axiom of determinacy, id=6516 -- WP: axiom of determinacy -- Status: A

… (former caveats have been rectified by Determinacy article) --Trovatore 03:17, 7 September 2005 (UTC)

• PM: Cantor-Bendixson derivative, id=6736 -- WP: Cantor-Bendixson derivative -- Status: A

Mathemens (talk) 22:34, 30 April 2008 (UTC)

• PM: Cantor-Bendixson theorem, id=6737 -- WP: Cantor-Bendixson theorem -- Status: A

Paul August ☎ 05:29, 28 May 2006 (UTC)

• PM: paradox of the binary tree, id=9332^new! -- WP guess: paradox of the binary tree -- Status:

[edit] 03E17 Cardinal characteristics of the continuum

All articles processed. Paul August ☎ 03:37, Mar 14, 2005 (UTC)

[edit] 03E20 Other classical set theory (including functions, relations, and set algebra)

Needs to be merged: 15. Paul August ☎ 17:03, August 25, 2005 (UTC)

Needs to be copied: 2. Paul August ☎ 17:03, August 25, 2005 (UTC)

• PM: additive, id=3400 -- WP: sigma additivity -- Status: C

Paul August ☎ 00:48, August 27, 2005 (UTC)

• PM: antisymmetric, id=1666 -- WP: antisymmetric -- Status: A

The PM article gives some finite examples, and gives fromulas for the number of relations and antisymmetric relations on a set with n elements. This content could be included, but I'm not sure it needs to be. Paul August ☎ 14:37, Mar 15, 2005 (UTC)

• PM: complex function, id=6226 -- WP: complex analysis -- Status: A

The PM articles content is covered in complex analysis, real part and imaginary part. We could, however, make complex function its own article. Paul August ☎ 13:45, Mar 17, 2005 (UTC)

• PM: constant function, id=4727 -- WP: constant function -- Status: M

Paul August ☎ 04:54, Mar 18, 2005 (UTC)

• PM: dependence relation, id=5792 -- WP: dependence relation -- Status: NC

This topic is related to Matroids. Paul August ☎ 16:50, August 25, 2005 (UTC)

The only article linking to dependence relation is on using the term in a way that suggests redirecting to statistical independence, not the concept occuring in matroid theory. Should this become a disambiguation page? Michael Hardy 20:49, August 31, 2005 (UTC)

Perhaps, I don't know much about this. Paul August ☎ 22:54, August 31, 2005 (UTC)

• PM: direct image, id=443 -- WP: image (mathematics) -- Status: A

Paul August ☎ 05:06, Mar 18, 2005 (UTC)

• PM: domain, id=966 -- WP: domain (mathematics) -- Status: NM

The PM article contains the more general notion of domain of a relation. Paul August ☎ 01:02, Apr 23, 2005 (UTC)

• PM: dynkin system, id=2024 -- WP: Dynkin system -- Status: C

Paul August ☎ 01:56, August 27, 2005 (UTC)

• PM: equivalence class, id=468 -- WP: equivalence class -- Status: A

Paul August ☎ 01:12, Apr 23, 2005 (UTC)

• PM: fibre, id=3276 -- WP: Image (mathematics) -- Status: M

Paul August ☎ 02:26, Apr 23, 2005 (UTC)

• PM: filtration, id=1331 -- WP: filtration (abstract algebra) -- Status: A

Paul August ☎ 16:15, Apr 23, 2005 (UTC)

• PM: finite character, id=3692 -- WP: set system of finite character -- Status: C

Paul August ☎ 02:59, August 27, 2005 (UTC)

• PM: fix (transformation actions), id=2510 -- WP: transformation (mathematics) -- Status: NM

Paul August ☎ 16:27, August 25, 2005 (UTC)

• PM: function, id=360 -- WP: function (mathematics) -- Status: A

Paul August ☎ 03:41, Apr 29, 2005 (UTC)

• PM: functional, id=2722 -- WP: functional -- Status: A

Paul August ☎ 13:23, August 5, 2005 (UTC)

• PM: generalized cartesian product, id=361 -- WP: Cartesian product -- Status: M

Paul August ☎ 18:34, August 8, 2005 (UTC)

• PM: graph, id=3701 -- WP: graph of a function -- Status: A

Paul August ☎ 20:37, Apr 23, 2005 (UTC)

• PM: identity map, id=5418 -- WP: identity function -- Status: NM

Paul August ☎ 15:38, August 5, 2005 (UTC)

• PM: inclusion mapping, id=4402 -- WP: inclusion map -- Status: A

Paul August ☎ 01:32, August 16, 2005 (UTC)

• PM: inductive set, id=386 -- WP: inductive set (axiom of infinity) -- Status: C

PM article is just a definition, but Mathworld has a nice article. Paul August ☎ 01:33, August 28, 2005 (UTC)

• PM: invariant, id=2504 -- WP: invariant -- Status: NM

Paul August ☎ 17:45, August 7, 2005 (UTC)

• PM: inverse function theorem, id=3346 -- WP: inverse function theorem -- Status: NM

Paul August ☎ 17:50, August 7, 2005 (UTC)

• PM: inverse image, id=442 -- WP: image (mathematics) -- Status: NM

Paul August ☎ 17:55, August 7, 2005 (UTC)

• PM: law of trichotomy, id=5668 -- WP: trichotomy -- Status: A

I think the WP article needs some work though. Paul August ☎ 18:12, August 7, 2005 (UTC)

• PM: left function notation, id=1349 -- WP: mathematical function -- Status: NM

Or perhaps merged with the PM article right function notation (below) into it's own article say function notation. Paul August ☎ 16:14, August 25, 2005 (UTC)

• PM: level set, id=6569 -- WP: level set -- Status: NM

PM defines level set as a synonym of fiber. Our article has a more restrictive definition. I don't know which is more correct, but this should be reconciled, and if the fiber definition is common, it should be mentioned in our article. Paul August ☎ 16:13, August 8, 2005 (UTC)

• PM: mapping, id=1975 -- WP: map (mathematics) -- Status: A

Paul August ☎ 19:05, August 7, 2005 (UTC)

• PM: mapping of period n is a bijection, id=4540 -- WP: function composition -- Status: NM

Paul August ☎ 19:41, August 7, 2005 (UTC)

• PM: operation, id=6653 -- WP: operator -- Status: A

Paul August ☎ 19:48, August 7, 2005 (UTC)

• PM: partial function, id=3341 -- WP: partial function -- Status: A

Paul August ☎ 20:34, August 7, 2005 (UTC)

• PM: partial mapping, id=4768 -- WP: partial mapping -- Status: NM

partial mapping redirects to partial function. The PM article is about an entirely different thing, which should probably be merged into WP in some form. Paul August ☎ 16:13, August 8, 2005 (UTC)

• PM: period of mapping, id=4539 -- WP: function composition -- Status: NM

Paul August ☎ 19:41, August 7, 2005 (UTC)

• PM: pi-system, id=2037 -- WP: pi-system -- Status: A

Paul August ☎ 17:18, August 8, 2005 (UTC)

NC changed to A, its now in WP of its own accord. linas 04:49, 24 November 2006 (UTC)

• PM: proof of inverse function theorem, id=4112 -- WP: inverse function theorem -- Status: NM

This proof might (or might not) be useful. Paul August ☎ 16:13, August 8, 2005 (UTC)

• PM: proof of the associativity of the symmetric difference operator, id=6192 -- WP: none -- Status: N

Paul August ☎ 17:28, August 8, 2005 (UTC)

• PM: proper subset, id=501 -- WP: proper subset -- Status: A

Paul August ☎ 03:25, Apr 29, 2005 (UTC)

• PM: range, id=967 -- WP: range (mathematics) -- Status: NM

The PM article defines the more general notion of range of a relation. Paul August ☎ 19:27, August 8, 2005 (UTC)

• PM: reflexive, id=1644 -- WP: reflexive -- Status: A

Paul August ☎ 19:39, August 8, 2005 (UTC)

• PM: relation, id=122 -- WP: relation (mathematics) -- Status: A

Paul August ☎ 20:03, August 8, 2005 (UTC)

• PM: restriction, id=4401 -- WP: function (mathematics) -- Status: A

Paul August ☎ 21:07, August 10, 2005 (UTC)

• PM: right function notation, id=1351 -- WP: function (mathematics) -- Status: NM

Or perhaps merged with the PM article left function notation (above) into it's own article say function notation. Paul August ☎ 16:14, August 25, 2005 (UTC)

• PM: set difference, id=913 -- WP: complement (set theory) -- Status: A

Paul August ☎ 19:06, May 20, 2005 (UTC)

• PM: symmetric, id=1647 -- WP: symmetric relation -- Status: A

Paul August ☎ 01:39, August 16, 2005 (UTC)

• PM: symmetric difference, id=916 -- WP: symmetric difference -- Status: A

Paul August ☎ 01:51, August 16, 2005 (UTC)

• PM: the inverse image commutes with set operations, id=4213 -- WP: image (mathematics) -- Status: NM

Paul August ☎ 16:18, August 25, 2005 (UTC)

• PM: transformation, id=1977 -- WP: transformation (mathematics) -- Status: A

Paul August ☎ 01:59, August 16, 2005 (UTC)

• PM: transitive, id=1565 -- WP: transitive set -- Status: A

Paul August ☎ 03:38, August 25, 2005 (UTC)

• PM: transitive, id=1669 -- WP: transitive relation -- Status: A

Paul August ☎ 03:41, August 25, 2005 (UTC)

• PM: transitive closure, id=3486 -- WP: transitive set -- Status: A

PM gives a construction of the transitive closure of a set and our article should probably include one, but I'm not sure that the PM one is correct. Paul August ☎ 15:58, August 25, 2005 (UTC)

• PM: antiderivative of complex function, id=7140 -- WP: antiderivative of complex function -- Status: A

I wrote a new article inspired by the PM article. Oleg Alexandrov (talk) 01:49, 21 July 2006 (UTC)

• PM: Characterization of basis of finite dimensional vector space, id=7247 -- WP guess: Characterization of basis of finite dimensional vector space -- Status:

• PM: constant functions and continuity, id=7088 -- WP guess: constant functions and continuity -- Status:

• PM: level sets of smooth functions on manifolds, id=7148 -- WP guess: level sets of smooth functions on manifolds -- Status:

• PM: limit of sequence of sets, id=6715 -- WP guess: limit of sequence of sets -- Status:

• PM: properties of functions, id=6705 -- WP guess: properties of functions -- Status:

• PM: argument, id=8185^new! -- WP guess: argument -- Status:

• PM: criterion for a set to be transitive, id=8429^new! -- WP guess: criterion for a set to be transitive -- Status:

• PM: example of antisymmetric, id=8044^new! -- WP guess: example of antisymmetric -- Status:

• PM: example of law of trichotomy on <, id=9586^new! -- WP guess: [[example of law of trichotomy on <]] -- Status:

• PM: examples of ring of sets, id=7759^new! -- WP guess: examples of ring of sets -- Status:

• PM: finite fields of sets, id=7758^new! -- WP guess: finite fields of sets -- Status:

• PM: irreflexive, id=7639^new! -- WP guess: irreflexive -- Status:

• PM: operations on relations, id=8600^new! -- WP guess: operations on relations -- Status:

• PM: pointed set, id=7936^new! -- WP guess: pointed set -- Status:

• PM: product, id=7710^new! -- WP guess: product -- Status:

• PM: properties of a function, id=8497^new! -- WP guess: properties of a function -- Status:

• PM: properties of injective functions, id=8879^new! -- WP guess: properties of injective functions -- Status:

• PM: quasi-inverse of a function, id=8509^new! -- WP guess: quasi-inverse of a function -- Status:

• PM: ring of sets, id=7757^new! -- WP guess: ring of sets -- Status:

• PM: Schröeder Bernstein Theorem: Proof, id=8884^new! -- WP guess: Schröeder Bernstein Theorem: Proof -- Status:

• PM: well-founded relation, id=9781^new! -- WP guess: well-founded relation -- Status:

[edit] 03E25 Axiom of choice and related propositions

• PM: axiom of choice, id=310 -- WP: axiom of choice -- Status: NM

Paul August ☎ 20:37, August 28, 2005 (UTC)

• PM: axiom of countable choice, id=6418 -- WP: axiom of countable choice -- Status: M

Paul August ☎ 21:42, August 28, 2005 (UTC)

• PM: choice function, id=6419 -- WP: choice function -- Status: M

Paul August ☎ 00:24, August 29, 2005 (UTC)

• PM: Zorn's lemma and the well-ordering theorem equivalence of Hausdorff's maximum principle, id=3493 -- WP guess: Zorn's lemma and the well-ordering theorem equivalence of Hausdorff's maximum principle -- Status: NC

Needs to be copied or merged into some article, not sure where. linas 02:36, 8 April 2007 (UTC)

• PM: equivalence of Zorn's lemma and the axiom of choice, id=3358 -- WP: Zorn's lemma -- Status: NM

Zorn's lemma has a sketch of a proof that AC implies Zorn, I think it would be good to include the reverse implication. Paul August ☎ 04:07, August 31, 2005 (UTC)

• PM: Hausdorff's maximum principle, id=3491 -- WP: Hausdorff maximality theorem -- Status: A

PM has a proof using Zorn's lemma, which would be good to include. Paul August ☎ 04:45, August 31, 2005 (UTC)

Changed from NM to A, as I just added text that is more or less equivalent, I think. linas 02:18, 8 April 2007 (UTC)

• PM: Kuratowski's lemma, id=3695 -- WP guess: Kuratowski's lemma -- Status:

• PM: maximality principle, id=2533 -- WP guess: maximality principle -- Status:

• PM: permutation model, id=6428 -- WP guess: permutation model -- Status:

• PM: principle of finite induction, id=245 -- WP: mathematical induction -- Status: A

Paul August ☎ 20:20, August 31, 2005 (UTC)

• PM: principle of finite induction proven from well-ordering principle, id=337 -- WP guess: principle of finite induction proven from well-ordering principle -- Status:

• PM: proof of Tukey's lemma, id=4672 -- WP guess: proof of Tukey's lemma -- Status:

• PM: proof of Zermelo's well-ordering theorem, id=3359 -- WP: well-ordering theorem -- Status: NM

Paul August ☎ 20:29, August 31, 2005 (UTC)

• PM: Tukey's lemma, id=3693 -- WP guess: Tukey's lemma -- Status:

• PM: Zermelo's postulate, id=3694 -- WP guess: Zermelo's postulate -- Status:

• PM: Zermelo's well-ordering theorem, id=3354 -- WP: well-ordering theorem -- Status: A

Paul August ☎ 19:45, August 31, 2005 (UTC)

• PM: Zorn's lemma, id=1341 -- WP: Zorn's lemma -- Status: A

Paul August ☎ 04:01, August 31, 2005 (UTC)

• PM: Hausdorff paradox, id=7057 -- WP guess: Hausdorff paradox -- Status:

• PM: proof of Banach-Tarski paradox, id=7123 -- WP guess: proof of Banach-Tarski paradox -- Status:

• PM: proof of Hausdorff paradox, id=7059 -- WP guess: proof of Hausdorff paradox -- Status:

• PM: relation as union of functions, id=7241 -- WP guess: relation as union of functions -- Status:

• PM: one-to-one function from onto function, id=8604^new! -- WP guess: one-to-one function from onto function -- Status:

• PM: proof of Zermelo's postulate, id=8342^new! -- WP guess: proof of Zermelo's postulate -- Status:

• PM: proof that a relation is union of functions if and only if AC, id=8763^new! -- WP guess: proof that a relation is union of functions if and only if AC -- Status:

• PM: selector, id=8792^new! -- WP guess: selector -- Status:

• PM: well-ordering principle for natural numbers proven from the principle of finite induction, id=8835^new! -- WP guess: well-ordering principle for natural numbers proven from the principle of finite induction -- Status:

• PM: well-ordering principle implies axiom of choice, id=8200^new! -- WP guess: well-ordering principle implies axiom of choice -- Status:

[edit] 03E30 Axiomatics of classical set theory and its fragments

• PM: \mathcal{U}-small, id=5658 -- WP guess: \mathcalU-small -- Status:

• PM: axiom of extensionality, id=4391 -- WP: axiom of extensionality -- Status: A

Paul August ☎ 04:17, Apr 29, 2005 (UTC)

• PM: axiom of infinity, id=4419 -- WP: axiom of infinity -- Status: NM

Paul August ☎ 02:35, 8 May 2006 (UTC)

• PM: axiom of pairing, id=4392 -- WP: axiom of pairing -- Status: A

Paul August ☎ 01:31, September 4, 2005 (UTC)

• PM: axiom of power set, id=4399 -- WP: axiom of power set -- Status: M

Paul August ☎ 19:09, 14 September 2005 (UTC)

• PM: axiom of union, id=4394 -- WP: axiom of union -- Status: A

Paul August ☎ 02:30, 8 May 2006 (UTC)

• PM: axiom schema of separation, id=4393 -- WP: axiom schema of separation -- Status: A

Paul August ☎ 02:26, 15 September 2005 (UTC)

• PM: de Morgan's laws, id=2308 -- WP guess: de Morgan's laws -- Status:

• PM: de Morgan's laws for sets (proof), id=4134 -- WP guess: de Morgan's laws for sets (proof) -- Status:

• PM: example of universe, id=5569 -- WP guess: example of universe -- Status:

• PM: set theory, id=3866 -- WP guess: set theory -- Status:

• PM: union, id=1619 -- WP: union (set theory) -- Status: A

• PM: universe, id=4107 -- WP guess: universe -- Status:

• PM: von Neumann-Bernays-Gödel set theory, id=4395 -- WP guess: von Neumann-Bernays-Gödel set theory -- Status:

• PM: example of universe of finite sets, id=6747 -- WP guess: example of universe of finite sets -- Status:

• PM: proof of properties of universe, id=7544 -- WP guess: proof of properties of universe -- Status:

• PM: Tarski's axiom, id=7548 -- WP guess: Tarski's axiom -- Status:

• PM: index of set theory, id=8883^new! -- WP guess: index of set theory -- Status:

• PM: well-foundedness and axiom of foundation, id=9800^new! -- WP guess: well-foundedness and axiom of foundation -- Status:

[edit] 03E35 Consistency and independence results

• PM: chain condition, id=3241 -- WP guess: chain condition -- Status:

• PM: composition of forcing notions, id=3256 -- WP guess: composition of forcing notions -- Status:

• PM: composition preserves chain condition, id=3262 -- WP guess: composition preserves chain condition -- Status:

• PM: equivalence of forcing notions, id=3257 -- WP guess: equivalence of forcing notions -- Status:

• PM: forcing, id=3039 -- WP guess: forcing -- Status:

• PM: forcing relation, id=3238 -- WP guess: forcing relation -- Status:

• PM: forcings are equivalent if one is dense in the other, id=3263 -- WP guess: forcings are equivalent if one is dense in the other -- Status:

• PM: FS iterated forcing preserves chain condition, id=3314 -- WP guess: FS iterated forcing preserves chain condition -- Status:

• PM: iterated forcing, id=3264 -- WP guess: iterated forcing -- Status:

• PM: iterated forcing and composition, id=3265 -- WP guess: iterated forcing and composition -- Status:

• PM: partial order with chain condition does not collapse cardinals, id=3242 -- WP guess: partial order with chain condition does not collapse cardinals -- Status:

• PM: proof of partial order with chain condition does not collapse cardinals, id=3243 -- WP guess: proof of partial order with chain condition does not collapse cardinals -- Status:

• PM: proof that forcing notions are equivalent to their composition, id=3258 -- WP guess: proof that forcing notions are equivalent to their composition -- Status:

[edit] 03E40 Other aspects of forcing and Boolean-valued models

• PM: complete partial orders do not add small subsets, id=3239 -- WP guess: complete partial orders do not add small subsets -- Status:

• PM: proof of complete partial orders do not add small subsets, id=3240 -- WP guess: proof of complete partial orders do not add small subsets -- Status:

[edit] 03E45 Inner models, including constructibility, ordinal definability, and core models

• PM: \Diamond is equivalent to \clubsuit and continuum hypothesis, id=3247 -- WP guess: \Diamond is equivalent to \clubsuit and continuum hypothesis -- Status:

• PM: Levy collapse, id=3244 -- WP guess: Levy collapse -- Status:

• PM: proof of \Diamond is equivalent to \clubsuit and continuum hypothesis, id=3248 -- WP guess: proof of \Diamond is equivalent to \clubsuit and continuum hypothesis -- Status:

[edit] 03E50 Continuum hypothesis and Martin's axiom

• PM: a shorter proof: Martin's axiom and the continuum hypothesis, id=4647 -- WP guess: a shorter proof: Martin's axiom and the continuum hypothesis -- Status:

• PM: continuum hypothesis, id=1183 -- WP: continuum hypothesis -- Status: A

Trovatore 15:25, 30 August 2005 (UTC)

• PM: generalized continuum hypothesis, id=1184 -- WP: continuum hypothesis -- Status: M

Paul August ☎ 01:44, 11 October 2005 (UTC)

• PM: Martin's axiom, id=3266 -- WP: Martin's axiom -- Status: A

Paul August ☎ 00:32, 11 October 2005 (UTC)

• PM: Martin's axiom and the continuum hypothesis, id=3270 -- WP guess: Martin's axiom and the continuum hypothesis -- Status:

• PM: Martin's axiom is consistent, id=3893 -- WP guess: Martin's axiom is consistent -- Status:

[edit] 03E55 Large cardinals

• PM: inaccessible cardinals, id=3221 -- WP: inaccessible cardinal -- Status: A

Trovatore 15:02, 30 August 2005 (UTC)

[edit] 03E65 Other hypotheses and axioms

• PM: \clubsuit, id=3246 -- WP: clubsuit -- Status:

• PM: \Diamond, id=3245 -- WP: ◊ -- Status:

• PM: combinatorial principle, id=5750 -- WP guess: combinatorial principle -- Status:

[edit] 03E70 Nonclassical and second-order set theories

All articles processed. Paul August ☎ 05:46, 28 May 2006 (UTC)

• PM: neutrosophic set, id=5844 -- WP: (none) -- Status: N

Apparently a deleted article. See also neutrosophic probability in 60A10 Probabilistic measure theory. Ben Cairns 06:07, 3 Feb 2005 (UTC).

• PM: neutrosophic set, id=7187 -- WP: none -- Status: N

A somewhat eccentric notion of Florentin Smarandache. Paul August ☎ 05:46, 28 May 2006 (UTC)

[edit] 03E72 Fuzzy set theory

• PM: fuzzy subset, id=8773^new! -- WP guess: fuzzy subset -- Status:

[edit] 03E75 Applications of set theory

[edit] 03E99 Miscellaneous

• PM: alternative characterization of filter, id=6339 -- WP: Filter (mathematics) -- Status: A

Paul August ☎ 04:21, Feb 13, 2005 (UTC)

• PM: class, id=4551 -- WP: class (set theory) -- Status: NM

Paul August ☎ 04:26, Feb 13, 2005 (UTC)

• PM: comparison of filters, id=6303 -- WP: Filter (mathematics) -- Status: NM

Paul August ☎ 04:30, Feb 13, 2005 (UTC)

• PM: complement, id=1919 -- WP: complement (set theory) -- Status: A

Paul August ☎ 04:32, Feb 13, 2005 (UTC)

• PM: concepts in set theory, id=5656 -- WP: set (et al) -- Status: A

Paul August ☎ 04:38, Feb 13, 2005 (UTC)

• PM: Dedekind infinite, id=1182 -- WP: Dedekind infinite -- Status: A

Paul August ☎ 04:44, Feb 13, 2005 (UTC)

• PM: delta system, id=3267 -- WP guess: delta system -- Status:

• PM: delta system lemma, id=3268 -- WP guess: delta system lemma -- Status:

• PM: diagonal intersection, id=3233 -- WP guess: diagonal intersection -- Status: C

Article helps the understanding of Fodor's lemma and club filter, so I copied and edited it; Porcher 17:25, 1 Apr 2005 (UTC)

• PM: disjoint union, id=5659 -- WP: disjoint union -- Status: NM

In fact the MP article should replace (almost) our article. Paul August ☎ 05:03, Feb 13, 2005 (UTC)

• PM: examples of filters, id=3259 -- WP: Filter (mathematics) -- Status: NM

Paul August ☎ 05:22, Feb 13, 2005 (UTC)

• PM: filter, id=1342 -- WP: filter (mathematics) -- Status: NM

Paul August ☎ 05:30, Feb 13, 2005 (UTC)

• PM: filter basis, id=6302 -- WP: filter (mathematics) -- Status: NM

The more common term (in my experience) is "filter base".Paul August ☎ 21:08, Feb 14, 2005 (UTC)

• PM: intersection, id=1630 -- WP: intersection (set theory) -- Status: A

Paul August ☎ 21:14, Feb 14, 2005 (UTC)

• PM: multiset, id=2090 -- WP: multiset -- Status: NM

Paul August ☎ 21:22, Feb 14, 2005 (UTC)

• PM: pairwise disjoint, id=5653 -- WP: pairwise disjoint -- Status: A

Paul August ☎ 21:26, Feb 14, 2005 (UTC)

• PM: proof of alternative characterization of filter, id=6340 -- WP: filter (mathematics) -- Status: NM

Paul August ☎ 21:30, Feb 14, 2005 (UTC)

• PM: proof of delta system lemma, id=3269 -- WP guess: proof of delta system lemma -- Status:

• PM: rational number, id=396 -- WP: rational number -- Status: A

Paul August ☎ 21:48, Feb 14, 2005 (UTC)

• PM: saturated (set), id=3275 -- WP guess: saturated (set) -- Status:

• PM: set, id=1635 -- WP: set -- Status: A

Paul August ☎ 22:09, Feb 14, 2005 (UTC)

• PM: superset, id=2585 -- WP: subset -- Status: A

Paul August ☎ 01:54, Feb 15, 2005 (UTC)

• PM: Zermelo-Fraenkel axioms, id=317 -- WP: Zermelo-Fraenkel axioms -- Status: A

Paul August ☎ 02:00, Feb 15, 2005 (UTC)

• PM: basic properties of a limit along a filter, id=7434 -- WP guess: basic properties of a limit along a filter -- Status:

• PM: construction of Banach limit using limit along an ultrafilter, id=7437 -- WP guess: construction of Banach limit using limit along an ultrafilter -- Status:

• PM: equation, id=7330 -- WP: equation -- Status: A

Paul August ☎ 02:26, 8 May 2006 (UTC)

• PM: every bounded sequence has limit along an ultrafilter, id=7435 -- WP guess: every bounded sequence has limit along an ultrafilter -- Status:

• PM: limit along a filter, id=7433 -- WP guess: limit along a filter -- Status:

• PM: algebraic system, id=7695^new! -- WP guess: algebraic system -- Status:

• PM: collection, id=8791^new! -- WP guess: collection -- Status:

• PM: cumulative hierarchy, id=8436^new! -- WP guess: cumulative hierarchy -- Status:

• PM: indexing set, id=8202^new! -- WP guess: indexing set -- Status:

• PM: multiplicative filter, id=9040^new! -- WP guess: multiplicative filter -- Status:

• PM: number of ultrafilters, id=7853^new! -- WP guess: number of ultrafilters -- Status:

• PM: section filter, id=8906^new! -- WP guess: section filter -- Status:

[edit] 03Exx Set theory

[edit] 03F03 Proof theory, general

• PM: \mathcal{NJ}p, id=3504 -- WP guess: \mathcalNJp -- Status:

• PM: \mathcal{NK}p, id=3506 -- WP guess: \mathcalNKp -- Status:

• PM: natural deduction, id=3503 -- WP: natural deduction -- Status: A

Paul August ☎ 02:11, Feb 15, 2005 (UTC)

• PM: sequent, id=3502 -- WP: sequent -- Status: M

Paul August ☎ 02:38, 21 September 2005 (UTC)

• PM: sound, complete, id=3445 -- WP guess: sound, complete -- Status:

• PM: Löb's theorem, id=9381^new! -- WP guess: Löb's theorem -- Status:

[edit] 03F07 Structure of proofs

• PM: circular reasoning, id=8174^new! -- WP guess: circular reasoning -- Status:

[edit] 03F15 Recursive ordinals and ordinal notations

[edit] 03F20 Complexity of proofs

• PM: switching lemma, id=4789 -- WP guess: switching lemma -- Status:

[edit] 03F30 First-order arithmetic and fragments

• PM: Elementary Functional Arithmetic, id=3302 -- WP guess: Elementary Functional Arithmetic -- Status:

• PM: PA, id=3301 -- WP: Peano arithmetic -- Status: A

Paul August ☎ 19:16, 6 January 2006 (UTC)

• PM: Peano arithmetic, id=2789 -- WP: Peano arithmetic -- Status: M

Jeekc 11:50, 12 November 2005 (UTC)

[edit] 03F35 Second- and higher-order arithmetic and fragments

NM: 1. Paul August ☎ 05:10, 31 May 2006 (UTC)

• PM: ACA_0, id=3310 -- WP: Second-order arithmetic -- Status: A

Paul August ☎ 05:10, 31 May 2006 (UTC)

• PM: RCA_0, id=3309 -- WP: Second-order arithmetic -- Status: A

Paul August ☎ 05:10, 31 May 2006 (UTC)

• PM: Z_2, id=3308 -- WP: Second-order arithmetic -- Status: A

Paul August ☎ 04:07, 31 May 2006 (UTC)

• PM: comprehension axiom, id=3307 -- WP: Axiom schema of specification -- Status: NM

Paul August ☎ 21:36, 4 October 2005 (UTC)

• PM: induction axiom, id=3306 -- WP: axiom of induction -- Status: C

The axiom of induction (or induction axiom) in its various forms is described in WP in several places: Peano axioms, second-order arithmetic, Kripke–Platek set theory, number system, but it should have its own article.

[edit] 03F55 Intuitionistic mathematics

• PM: inhabited set, id=5931 -- WP: inhabited set -- Status: A

Paul August ☎ 03:56, 31 May 2006 (UTC)

[edit] 03F60 Constructive and recursive analysis

NC: 1. Mathemens (talk) 22:46, 30 April 2008 (UTC)

• PM: computable real function, id=6248 -- WP: computable real function -- Status: C

Mathemens (talk) 22:46, 30 April 2008 (UTC)

• PM: computable sequence, id=6247 -- WP : computable sequence -- Status: NC

Paul August ☎ 20:42, 29 May 2006 (UTC)

[edit] 03Fxx Proof theory and constructive mathematics

[edit] 03G05 Boolean algebras

All articles processed. Paul August ☎ 05:37, 28 May 2006 (UTC)

• PM: Boolean ring, id=2602 -- WP: Boolean ring -- Status: A

CryptoDerk 15:56, Apr 30, 2005 (UTC)

• PM: M. H. Stone's representation theorem, id=3983 -- WP: Stone's representation theorem for Boolean algebras -- Status: A

Paul August ☎ 05:37, 28 May 2006 (UTC)

• PM: Boolean ideal, id=9319^new! -- WP guess: Boolean ideal -- Status:

[edit] 03G10 Lattices and related structures

All articles processed. Paul August ☎ 20:43, Apr 30, 2005 (UTC)

• PM: Boolean lattice, id=2594 -- WP: Boolean algebra -- Status: A

CryptoDerk 15:52, Apr 30, 2005 (UTC)

• PM: complete lattice, id=3304 -- WP: complete lattice -- Status: A

CryptoDerk 15:51, Apr 30, 2005 (UTC)

• PM: lattice, id=2593 -- WP: lattice (order) -- Status: A

CryptoDerk 15:50, Apr 30, 2005 (UTC)

• PM: bounded complete, id=9303^new! -- WP guess: bounded complete -- Status:

• PM: criteria for a poset to be a complete lattice, id=8832^new! -- WP guess: criteria for a poset to be a complete lattice -- Status:

• PM: De Morgan algebra, id=8238^new! -- WP guess: De Morgan algebra -- Status:

• PM: intersection structure, id=9406^new! -- WP guess: intersection structure -- Status:

[edit] 03G12 Quantum logic

• PM: commutativity relation in an orthocomplemented lattice, id=8943^new! -- WP guess: commutativity relation in an orthocomplemented lattice -- Status:

• PM: orthocomplemented lattice, id=7822^new! -- WP guess: orthocomplemented lattice -- Status:

• PM: orthomodular lattice, id=8735^new! -- WP guess: orthomodular lattice -- Status:

• PM: quantum logic, id=9056^new! -- WP guess: quantum logic -- Status:

[edit] 03G20 Lukasiewicz and Post algebras

[edit] 03G25 Other algebras related to logic

[edit] 03G30 Categorical logic, topoi

• PM: topos, id=8796^new! -- WP guess: topos -- Status:

[edit] 03G99 Miscellaneous

NM: 4. Paul August ☎ 20:24, 29 May 2006 (UTC)

• PM: biextensional collapse, id=3496 -- WP guess: Chu Space -- Status: NM

Paul August ☎ 20:24, 29 May 2006 (UTC)

• PM: Chu space, id=3495 -- WP: Chu space -- Status: NM

Paul August ☎ 20:24, 29 May 2006 (UTC)

• PM: Chu transform, id=3499 -- WP: Chu space -- Status: NM

Paul August ☎ 20:24, 29 May 2006 (UTC)

• PM: example of Chu space, id=3498 -- WP: Chu space -- Status: NM

Paul August ☎ 20:24, 29 May 2006 (UTC)

• PM: property of a Chu space, id=3497 -- WP guess: Chu space -- Status: NM

Paul August ☎ 20:24, 29 May 2006 (UTC)

[edit] 03Gxx Algebraic logic

[edit] 03H05 Nonstandard models in mathematics

• PM: non-standard analysis, id=8638^new! -- WP guess: non-standard analysis -- Status:

[edit] 03Hxx Nonstandard models