List of mathematical logic topics
From Wikipedia, the free encyclopedia
This is a list of mathematical logic topics, by Wikipedia page.
For traditional syllogistic logic, see the list of topics in logic. See also the list of computability and complexity topics for more theory of algorithms.
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Contents |
[edit] Working foundations
- Peano axioms
- Mathematical induction
- Naive set theory
- Universe (mathematics)
- Axiomatization
- Axiomatic system
- Axiomatic method
- Formal system
- Mathematical proof
- Tautology
- Consistency proof
- Arithmetization of analysis
- Foundations of mathematics
- Generating arithmetic
- Formal language
- Principia Mathematica
- Hilbert's program
- Impredicative
- Definable real number
- Algebraic logic
- Dialectica space
[edit] Model theory
- Cantor's back-and-forth method
- Functional predicate, monadic
- First-order predicate calculus
- Lindenbaum-Tarski algebra
- T-schema
- Maximal consistent set
- Compactness theorem
- Löwenheim-Skolem theorem
- Soundness theorem
- Gödel's completeness theorem
- Deduction theorem
- Elementary embedding
- Elementary substructure
- Löb's theorem
- Gödel's incompleteness theorem
- Ultraproduct
- Saturated model
- Non-standard model
- Non-standard arithmetic
- Non-standard calculus
- Non-standard analysis
- first-order logic
- Second-order logic
- Higher order logic
- Infinitary logic
- Finitary
- Finite model theory
- First-order arithmetic
- Second-order arithmetic
- Arithmetic set
- Whitehead problem
- Thompson groups
[edit] Set theory
- Algebra of sets
- Axiom of choice
- Boolean algebra (structure)
- Boolean-valued model
- Burali-Forti paradox
- Cantor's back-and-forth method
- Cantor's diagonal argument
- Cantor's first uncountability proof
- Cantor's theorem
- Cantor–Bernstein–Schroeder theorem
- Cardinality
- Cartesian product
- Class (set theory)
- Complement (set theory)
- Complete Boolean algebra
- Continuum (mathematics)
- Continuum hypothesis
- Countable set
- Descriptive set theory
- Determinacy
- Empty set
- Forcing (mathematics)
- Fuzzy set
- Internal set theory
- Intersection (set theory)
- L
- L(R)
- Large cardinal property
- Musical set theory
- Ordinal number
- Power set
- Russell's paradox
- Set theory
- Set
- Simple theorems in the algebra of sets
- Subset
- Θ (set theory)
- Tree (descriptive set theory)
- Tree (set theory)
- Union (set theory)
- Von Neumann universe
- Zero sharp
[edit] Descriptive set theory
[edit] Large cardinals
- Almost Ramsey cardinal
- Erdős cardinal
- Extendible cardinal
- Huge cardinal
- Hyper-Woodin cardinal
- Inaccessible cardinal
- Ineffable cardinal
- Mahlo cardinal
- Measurable cardinal
- N-huge cardinal
- Ramsey cardinal
- Rank-into-rank
- Remarkable cardinal
- Shelah cardinal
- Strong cardinal
- Strongly inaccessible cardinal
- Subtle cardinal
- Supercompact cardinal
- Superstrong cardinal
- Totally indescribable cardinal
- Weakly compact cardinal
- Weakly hyper-Woodin cardinal
- Weakly inaccessible cardinal
- Woodin cardinal
- Unfoldable cardinal
[edit] Recursion theory
- Entscheidungsproblem
- Decision problem
- Decidability (logic)
- Church-Turing thesis
- Recursive function
- Kleene's recursion theorem
- Recursively enumerable set
- Decidable language
- Undecidable language
- Rice's theorem
- Post's theorem
- Turing degree
- Effective results in number theory
- Diophantine set
- Matiyasevich's theorem
- Word problem for groups
- Arithmetical hierarchy
- Subrecursion theory
- Natural proof
- Hypercomputation
- Alonzo Church
- Emil Post
- Alan Turing
- Jacques Herbrand
- Haskell Curry
- Stephen Cole Kleene
- Definable real number
[edit] Proof theory
- Metamathematics
- Cut-elimination
- Tarski's indefinability theorem
- Diagonal lemma
- Provability logic
- Interpretability logic
- Sequent
- Sequent calculus
- Analytic proof
- Structural proof theory
- Self-verifying theories
- Substructural logics
- Proof-theoretic semantics
- Ludics
- System F
- Gerhard Gentzen
- Gentzen's consistency proof
- Reverse mathematics
- Nonfirstorderizability
- Interpretability
- Weak interpretability
- Cointerpretability
- Tolerant sequence
- Cotolerant sequence
[edit] Mathematical constructivism
- Nonconstructive proof
- Existence theorem
- Intuitionistic logic
- Intuitionistic type theory
- Type theory
- Lambda calculus
- Simply typed lambda calculus
- Typed lambda calculus
- Curry–Howard isomorphism
- Calculus of constructions
- Constructivist analysis
- Lambda cube
- System F
- Introduction to topos theory
- LF (logical framework)
- Computability logic
- Computable measure theory
- Finitism
- Ultraintuitionism
- Luitzen Egbertus Jan Brouwer
[edit] Modal logic
[edit] Theorem provers
- First-order resolution
- Automated theorem proving
- ACL2 theorem prover
- E equational theorem prover
- Gandalf theorem prover
- HOL theorem prover
- Isabelle theorem prover
- LCF theorem prover
- Otter theorem prover
- Paradox theorem prover
- Vampire theorem prover
- Interactive proof system
- Mizar system
- QED project
- Coq
[edit] Discovery systems
- Autoclass
- Automated Mathematician
- Eurisko
