User:Chalst/tasks

From Wikipedia, the free encyclopedia

You have new messages (last change).

Contents

[edit] Next

  1. Incorporate new content at Stephen Schwartz (journalist):
    • Article move?
    • Use of term islamofascism
  2. Deal with comments at: User:Dbuckner/logic, Wikipedia:Peer review/Logic
  3. Start Predicate page displacing current disambig page. ~~ Oct 2005
  4. Start Wikipedia:WikiProject Logic --- 16 Jun 2005
  5. Check Trovatore's definition at Free Boolean algebra --- 2 Nov 2005

[edit] Article composition

[edit] Laws of Thought

Rewrite Boole's syllogistic

[edit] Sometime

[edit] Logic

[edit] en.wikipedia

  • Template for alternate categories (thanks to JesseW) ---- 20:32, 12 Nov 2004 (UTC)

[edit] Software

[edit] Mathematics

In order to show that the axioms of the class of algebras we consider capture exactly the collection of predicates we have in mind, a representation theorem is necessary. A representation theorem is a correspondence between an abstract algebra and its set-theoretical model. The first representation theorem is due to Cayley [Cay78] showing that every abstract group is isomorphic to a concrete group of permutations. A representation theorem for the algebra of all predicates was first proved by Lindenbaum and Tarski [Tar35]. They proved that a Boolean algebra is isomorphic to the collection of all subsets of some set if and only if it is complete and atomic. This general result restricts the class of Boolean algebras for which a concrete representation exists. It was Stone [Sto36] who first saw a connection between algebra and topology. He constructed from a Boolean algebra a set of points using prime ideals which can be made into a topological space in a natural way. Conversely, using a topology on a set of points he was able to construct a Boolean algebra. For certain topological spaces (later called Stone spaces) these constructions give an isomorphism. In a later paper [Sto37], Stone generalized this correspondence from Stone spaces to spectral spaces and from Boolean algebras to distributive lattices. Hofmann and Keimel [HK72] described the Stone representation theorem in a categorical framework showing a duality between the category of Boolean algebras and a sub-category of topological spaces. A representation theorem for Boolean algebras with operators has been considered by J'onsson and Tarski [JT51, JT52]. By means of an extension theorem they proved that operators on a Boolean algebra can be naturally extended to completely additive operators on a complete and atomic Boolean algebra.
Stone's representation theorem leaves open the problem of finding an abstract characterization of topological spaces. For every topological space, its lattice of open sets forms a frame. This fact leads Papert and Papert [PP58] to a representation theorem between spatial frames and sober spaces. Even further, Isbell [Isb72a] gives an adjunction between the category of topological spaces with continuous functions and the opposite category of frames with frame homomorphisms. This adjunction yields a duality between the category of sober spaces and the category of spatial frames.


[edit] Computer Science

  • Merge:
    1. Category:Turing Award Laureate into Category:Turing Award Laureate; and
    2. Category:Nobel Prize winners into Category:Nobel laureates. ---- 17 Nov 2004
  • Geometric logic, Boolean relation theory, Stone spaces, and Equilogical spaces ---- 17 Nov 2004
  • Equational logic, order-sorted logic, and rewriting logic ---- 7 Dec 2004
  • LISPy things:
    1. LISP macro systems: namespace issues from RPG's Technical Issues of Separation paper, history of macros (MacLisp, etc.), CL macros (DEFMACRO, FLET), Hygiene (Kohlbecker's algorithm, syntactic closures, macros that work, R4RS syntax-rules, syntax-case) ---- 15 Dec 2004
    2. LISP object systems: message passing vs. generic functions, MOPs (see list of current MOPs), Flavors, CommonLOOPS, RPG's CLOS paper Alex Shinn's summary, SICP objects are closures approach, scheme object systems (see CMU Scheme OO directory), Dylan's object system (see Kidd's tutorial, multiple inheritance superclass linearization proposal, compilation issues ---- 15 Dec 4004
  • Start page process algebra, and maybe parallelism and concurrency. ---- 18 Jan 2005

[edit] Journalism, Economics, Politics, Culture

[edit] Definitions of fascism

Purpose of article: to help disputes on the question of how similar fascism and communism are, and the question of the extent to which there is such a thing as "Islamofacsism) Article should consist of excerpts from:

'Classic' definitions:

1. Mussolini's What is Fascism, 1932;
2. George Orwell's What is Fascism, 1944, can't be much bettered as a piece pointing out how debauched uses of the term can be;
3. John T. Flynn's As We Go Marching, 1944: we have to point out the polemical intent of this definition, but it is still interesting.

Comparitive analyses:

1. Ernst Nolte's "Fascist-minimum" from Fascism In Its Epoch, 1963 (stangely absent from this article, despite seminal contribution);
2. Stanley Payne's criteria from Fascism: Comparison and Definition, 1980;
3. Roger Griffin's The Nature of Fascism, 1991, and maybe also from his 1995 book. -- Jan 2006

[edit] Process

[edit] Disputed WP:DRV outcomes

Retrieved from "http://en.wikipedia.org../../../c/h/a/User%7EChalst_tasks_c8a6.html"