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  1. THE CONSISTENCY OF THE AXIOM OF CHOICE AND OF THE GENERALIZED CONTINUUM-HYPOTHESIS WITH THE AXIOMS OF SET THEORY. Annals of Mathematics Studies, No. 3. by Kurt (Goedel, Kurt) Godel, 1953-01-01
  2. An axiomatization of the generalized Edgeworth-Pareto principle in terms of choice functions [An article from: Mathematical Social Sciences] by V.D. Noghin, 2006-09-01
  3. Equivalents of the Axiom of Choice by H. & J. Rubin, 1963
  4. The consistency of the axiom of choice and of the generalized continuum-hypothesis with the axioms of set theory, (Annals of mathematics studies) by Kurt Gödel, 1949
  5. Zorn's Lemma: Max August Zorn, Kazimierz Kuratowski, Zermelo?Fraenkel Axioms, Axiom of Choice, Hausdorff Maximal Principle
  6. The Independence of the Axiom of Choice by Elliott Mendelson, 1955
  7. The independence of the axiom of choice by Paul J Cohen, 1959
  8. Wac?aw Sierpi?ski: Moscow, Russia, Jew, Set Theory, Axiom of Choice, Continuum Hypothesis, Number Theory, Function, Topology, Fractal, Sierpinski Triangle
  9. The Consistency of the Axiom of Choice and of the Generalized Continuum- Hypothesis with the Axioms of Set Theory by Kurt Godel, 1961
  10. The relationship between Luce's Choice axiom, Thurstone's Theory of comparative judgment, and the double exponential distribution (Social sciences working papers) by John I Yellott, 1975
  11. Large cardinals without the axiom of choice (Massachusetts Institute of Technology. Dept. of Mathematics. Thesis. 1976. Ph. D) by Everett Layton Bull, 1976
  12. Equivalents of the Axiom of Choice by Herman; Jean E. Rubin Rubin, 1963
  13. Stone??ech Compactification: Hausdorff Space, Tychonoff Space, Axiom of Choice, Marshall Harvey Stone, Universal Property, Continuous Function, Functor, Tychonoff's Theorem
  14. Equivalences of the axiom of choice by Stephanie Keyes, 1964

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22. Math Forum Discussions - Arbitrarily Weak Axiomatic Foundations?
on the following page http//en.wikipedia.org/wiki/axiom_of_choice . page http//en.wikipedia.org/wiki/axiom_of_choice Law_of_the_excluded .
http://mathforum.org/kb/search!execute.jspa?q=foundational&objID=f13&forumID=13&

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24. A Poosible Additional Axiom To ZFC?
http//en.wikipedia.org/wiki/axiom_of_choice Let X be a collection of nonempty sets. There exists a choice function f defined on X such that for each
http://www.mathkb.com/Uwe/Forum.aspx/math-logic/1243/A-poosible-additional-axiom
Home Contact Us FAQ Link to Us ... Discussion Groups Mathematics General Topics Research Operations Research Statistics ... Recreational Math Math Software Maple Mathematica MATLAB Scilab ... December 2004 Tip: Looking for answers? Try searching our database.
A poosible additional axiom to ZFC?
Thread view: Tree View List View (postings sorted by date) Single Message View Enable EMail Alerts Start New Thread Thread rating: uweWriteArtHdr('','','',1) namducnguyen - 10 Nov 2004 06:28 GMT Could ZFC be added with a new axiom which would say something to the effect
that if a choice function c exists solely on the basis of AC, then c is
unique?
If we could, how would we formulate such a new axiom?
Thanks.
-Nam
Reply to this Message uweWriteArtHdr('#nyikd168565Pl43483pd7tw1no','','#4tudnfEfjt_2cAzcRVnrgrcnnet',3) Peter Webb - 10 Nov 2004 07:09 GMT
[quoted text clipped - 4 lines]
Its hard to see how a system with this additional axiom could generally be
consistent.
For example, if we are choosing Real numbers R_n each from an infinite set of Reals, then R_1, R_2, R_3 ... may be one choice function, and

25. Axiom Of Choice Domain References On Wikipedia
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I think what that the second guy has to say about the a href= http//en.wikipedia. org/wiki/axiom_of_choice Axiom of Choice /a is hooey, which makes me
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30. Axiom Of Choice - ᏗᎪᏪᎵ ᎦᏧᎾᎳ ᎦᏚ
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Axiom of choice
Axiom of Choice This article is about the mathematical concept. For the band named after it, see Axiom of Choice (band) axiom (ᎧᏁᎬᎢ) ᎠᏑᏰᏛ AC axiom (ᎧᏁᎬᎢ) . Intuitively (ᎠᏓᏅᏖᏗ) ᎦᏬᏂᏍᎬ, ᎯᎠ axiom (ᎧᏁᎬᎢ) ᎠᏑᏰᏛ ᎠᏗᎭ Ꮎ ᎠᏓᏁᎸ ᏂᎦᎵᏍᏗᏍᎬᎫ ᎤᏓᏂᏝᏅ bins (ᏧᎬᏩᎶᏗ ᎠᎦᏘᏯ), ᎠᏂᏏᏴᏫᎭ ᎢᎦᎢ ᏕᎨᏒᎢ ᎤᏍᏗ ᏌᏊ ᏗᎦᏘᎴᏍᏗ, ᎧᎵ ᏗᏙᎳᎩ ᏌᏊ ᏗᎦᏘᎴᏍᏗ ᏰᎵᏇ ᎾᏍᏋ ᎠᏑᏰᏛ ᏂᏛᎴᏅᏓ ᎠᏂᏏᏴᏫᎭ bin (ᏧᎬᏩᎶᏗ ᎠᎦᏘᏯ), ᎢᏧᎳᎭ ᎢᏳᏃ ᏀᎾᎢ infinitely (ᎢᎪᎯᏓ ᎨᏒ) ᎤᎪᏗᏗ bins (ᏧᎬᏩᎶᏗ ᎠᎦᏘᏯ) ᎠᎴ ᎤᏚᎳᏗ Ꮭ "ᎠᏍᏓᏩᏛᏍᏙᏗ" ᎾᏍᎩᎾᎢ ᎦᏙ ᎤᏍᏗ ᏂᎦᎸᏉᏛᎾ ᎠᏑᏰᏍᏗ ᏂᏛᎴᏅᏓ ᎠᏂᏏᏴᏫᎭ. ᎯᎠ axiom (ᎧᏁᎬᎢ) ᎠᏑᏰᏛ ᎨᏒᎢ ᎬᏙᏗ ᎢᏳᏃ ᎯᎠ ᏎᏍᏗ bins (ᏧᎬᏩᎶᏗ ᎠᎦᏘᏯ) ᎨᏒᎢ finite (ᏎᏍᏗ) ᎠᎴ ᎢᏳᏃ ᏯᏛᎿ ᎠᏑᏰᏍᏗ "ᎠᏍᏓᏩᏛᏍᏙᏗ" ᎨᏒᎢ ᏰᎵ ᎠᏩᏛᏗ. ᎾᏍᎩ ᏥᏄᏍᏛᎩ formulated (ᎠᏃᏪᎵᏍᎬ) ᎭᏫᎾᏗᏢ 1904 ᎾᎥᎢ Ernst Zermelo ᏀᎢᏳᎢ ᎾᏍᎩ ᏥᏄᏍᏛᎩ ᎠᎴᏅᏔᏅ controversial (ᎠᏓᏅᏖᏗ), ᎾᏍᎩ ᎨᏒᎢ ᎾᏊ ᎬᏔᏅᎯ ᏄᏠᏯᏍᏛᎾ ᎧᏃᎯᏴᎯ ᎾᎥᎢ ᎤᎪᏗᏗ mathematicians (ᏗᏎᏍᏗ).

31. Reference For Axiom Of Choice - Search.com
a/x/i/axiom_of_choice.html . Categories Axiom of choice Model theory. help. advanced search » preferences ». search within these results
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Axiom of choice
From Wikipedia, the free encyclopedia
In mathematics , the axiom of choice , or AC , is an axiom of set theory . Intuitively speaking, AC says that given a collection of bins each containing at least one object, exactly one object from each bin can be picked and gathered in another bin—even if there are infinitely many bins and there is no "rule" for which object to pick from each. AC is not required if the number of bins is finite or if such a selection "rule" is available. It was formulated in 1904 by Ernst Zermelo While it was originally controversial, it is now used without reservation by most mathematicians. However, there are schools of mathematical thought, primarily within set theory, that either reject the axiom of choice or investigate consequences of axioms inconsistent with AC.
Contents
The axiom of choice states:
Let X be a set of non-empty sets . Then we can choose a single member from each set in X
A choice function is a function f on a collection of sets X such that for every set s in X f s ) is an element of s . With this concept, the axiom can be stated:

32. TPTP Syntax
intro_type definition axiom_of_choice tautology assumption %This should be used to record the symbol being defined, or the function
http://www.cs.miami.edu/~tptp/TPTP/SyntaxBNF.html
%v3.4.0.1 (TPTP version.internal development number)
%README ... this header provides important meta- and usage information
%Intended uses of the various parts of the TPTP syntax are explained
%in the TPTP technical manual, linked from www.tptp.org.
%Four kinds of separators are used, to indicate different types of rules:
% ::= is used for regular grammar rules, for syntactic parsing.
% :== is used for semantic grammar rules. These define specific values
% that make semantic sense when more general syntactic rules apply.
% ::- is used for rules that produce tokens.
% ::: is used for rules that define character classes used in the
% construction of tokens. %White space may occur between any two tokens. White space is not specified %in the grammar, but there are some restrictions to ensure that the grammar %read/1. %occur between any two tokens, but do not act as white space. Comments %will normally be discarded at the lexical level, but may be processed %by systems that understand them (e.g., if the system comment convention %is followed).

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35. Comp.compilers: Problem With Flex, Parsing A Large File
axiom_of_choice { return TK_axiom_of_choice ; } axiom { return TK_AXIOM ; } cnf { return TK_CNF ; } conjecture { return TK_CONJECTURE ; }
http://compilers.iecc.com/comparch/article/06-02-036
Problem with flex, parsing a large file
3 Feb 2006 18:43:44 -0500
From comp.compilers
Related articles Problem with flex, parsing a large file Re: Problem with flex, parsing a large file Re: Problem with flex, parsing a large file List of all articles for this month From: Newsgroups: comp.compilers Date: 3 Feb 2006 18:43:44 -0500 Organization: Compilers Central Keywords: flex, question Posted-Date: 03 Feb 2006 18:43:44 EST Dear all,
I am writing a compiler for TSTP, a small language (or format), for
theorem provers. I am using flex-2.5.4 and GNU bison-1.28, and I am
encountering a problem that seems to be related to flex.
Currently, I have developped the following files:
- tstp.lex: input to flex
- tstp.y: input to bison
- test.c: a program that open a given file, and calls the generated
parser on this file.
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37. Wiki Axiom Of Choice
Wiki Axiom of choice. Contents 1. Statement 1. 1. Variants 2. Usage 3. Drawbacks 3. 1. Alternatives Weaker forms 4. Independence 5. Stronger axioms
http://wapedia.mobi/en/Axiom_of_choice
Wiki: Axiom of choice Contents:
1. Statement

1. 1. Variants

2. Usage

3. Nonconstructive aspects
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38. Undecidable Statement Made Into Axiom? Text - Physics Forums Library
http//en.wikipedia.org/wiki/axiom_of_choice Independence_of_AC quote from article By work of Kurt Gödel and Paul Cohen, the axiom of choice is logically
http://www.physicsforums.com/archive/index.php/t-112083.html
Physics Help and Math Help - Physics Forums Mathematics Set Theory, Logic, Probability, Statistics PDA View Full Version : undecidable statement made into axiom? gravenewworld i am a little bit confused on 1 thing. can a statement that is undecidable in a axiomatic system just be added as a axiom to the original system and never lead to a contridiction?
this is the wiki article that is confusing me-
http://en.wikipedia.org/wiki/Axiom_of_choice#Independence_of_AC
quote from article: "By work of Kurt Gödel and Paul Cohen, the axiom of choice is logically independent of the other axioms of Zermelo-Fraenkel set theory (ZF). This means that neither it nor its negation can be proven to be true in ZF. Consequently, assuming the axiom of choice, or its negation, will never lead to a contradiction that could not be obtained without that assumption."
so if the CH( or ~CH) can be added to ZFC(since it was proven independent just like AC), then why is it still unsolved? Hurkyl i am a little bit confused on 1 thing. can a statement that is undecidable in a axiomatic system just be added as a axiom to the original system and never lead to a contridiction?
You are correct.

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40. Search Results From CDconnection.com For Axiom Of Choice.
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Axiom Of Choice
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3 matches or close matches found in 6 separate searches in 0.11 seconds. Axiom Of Choice Beyond Denial
CD
In Stock 9 Tracks Details Add to Basket 12/1999 X Dot 25 1002
Reg. Price: $12.06 CDC Part#: 245695 Axiom Of Choice Niya Yesh
CD
In Stock 9 Tracks Details Add to Basket 5/2000 Narada Records 49289
List Price: $16.98 CDC Part#: 438220 Axiom Of Choice Unfolding
CD
In Stock 10 Tracks Details Add to Basket 8/2002 Narada Records 12581
List Price: $16.98 CDC Part#: 722355 CDconnection.com

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