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1. 03E: Set Theory
Somewhat related to the ordering of sets is Combinatorial Set Theory. relations, and set algebra); 03E25 Axiom of choice and related propositions
http://www.math.niu.edu/~rusin/known-math/index/03EXX.html

2. PlanetMath: Axiom Of Choice
AMS MSC, 03E25 (Mathematical logic and foundations Set theory Axiom of choice and related propositions). 03E30 (Mathematical logic and foundations
http://planetmath.org/encyclopedia/AxiomOfChoice.html

3. 03Exx
03E25 Axiom of choice and related propositions See also 04A25; 03E30 Axiomatics 03E45 Constructibility, ordinal definability, and related notions
http://www.ams.org/mathweb/msc1991/03Exx.html

4. Sachgebiete Der AMS-Klassifikation: 00-09
and structures 03C10 Quantifier elimination and related topics 03C13 Finite classical set theory 03E25 Axiom of choice and related propositions,
http://www.math.fu-berlin.de/litrech/Class/ams-00-09.html

5. MathNet-Mathematical Subject Classification
03E25, Axiom of choice and related propositions See also 04A25. 03E30, Axiomatics of classical set theory and its fragments
http://basilo.kaist.ac.kr/API/?MIval=research_msc_1991_out&class=03-XX

6. Is Godel Lieing When He States This - Sci.logic | Google Groups
undecidable propositions of principia mathematica and related systems in The undecidable , M, Davis, Raven Press, 1965,p.21. and in Axiom of choice

7. DC MetaData For: The Ascoli Theorem Is Equivalent To The Boolean Prime Ideal The
MSC 54A35 Consistency and independence results, See also {03E35} 54D30 Compactness 03E25 Axiom of choice and related propositions, See also {04A25}
http://ftp.math.uni-rostock.de/pub/MetaFiles/herrlich-51.html

8. Jolly Roger Great Books Forums - 5 Reasons Why Godels Incompleteness Theorem Inv
reducibility which is invalid, he uses the Axiom of choice, he propositions of principia mathematica and related systems in The

9. Variations On Realizability: Realizing The Propositional Axiom Of Choice
Realizability and related functional interpretations provide models for these models do not validate the Axiom of choice for propositions taken over
http://portal.acm.org/citation.cfm?id=966869

10. Mhb03.htm
03E25, Axiom of choice and related propositions. 03E30, Axiomatics of classical set theory and its fragments. 03E35, Consistency and independence results
http://www.mi.imati.cnr.it/~alberto/mhb03.htm

11. List KWIC DDC22 510 And MSC+ZDM E-N Lexical Connection
Axiom of choice and related propositions 03E25 Axiomatic and generalized convexity 52A01 Axiomatic computability and recursion theory abstract and 03D75
http://www.math.unipd.it/~biblio/kwic/msc-cdd/dml2_11_05.htm

12. 03Exx
and set algebra) 03E25 Axiom of choice and related propositions 03E30 and Axioms 03E70 Nonclassical and secondorder set theories 03E72 Fuzzy set
http://www.emis.de/MSC2000/03Exx.html

13. HeiDOK
03E25 Axiom of choice and related propositions ( 0 Dok. ) 03E30 Axiomatics of classical set theory and its fragments ( 0 Dok.
http://archiv.ub.uni-heidelberg.de/volltextserver/msc_ebene3.php?zahl=03E&anzahl

14. VOLUME 1, NUMBER 2 (1990), Formalized Mathematics, ISSN 0777-4028
Zermelo Theorem and Axiom of choice, Formalized Mathematics 1(2), pages 265267, . Some simple propositions related to the introduced notions are proved.
http://mizar.uwb.edu.pl/fm/1990-1/fm1-2.html

15. Seminars Of The CENTRE De RECHERCHE En THEORIE Des CATEGORIES
the Axiom of choice for (Kuratowski)finite sets and ``related issues . However, in settings where the propositions themselves can be circular,
http://www.math.mcgill.ca/rags/seminar/seminar.listings.01

16. Harvard University Press: From Frege To Gödel : A Source Book In Mathematical Lo
The notion definite and the independence of the Axiom of choice On formally undecidable propositions of Principia mathematica and related systems I,
http://www.hup.harvard.edu/catalog/VANFGX.html?show=contents

17. On Gödel's Philosophy Of Mathematics, Notes
K. Gödel, On Formally Undecidable propositions of Principia Mathematica and related . Gödel, The Consistency of the Axiom of choice and the Generalized
http://www.friesian.com/goedel/notes.htm

18. Schaum's Outline Of Set Theory And Related Topics (McGraw-Hill) Doi:10.1036/0070
Master set theory and related topics with Schaumsthe highperformance study guide. Axiom of choice. Paradoxes in Set Theory. Algebra of propositions.
http://dx.doi.org/10.1036/0070379866

19. Godels Incompleteness Theorems Are A Complete Failure And Invalid - Sci.logic |
and the axioms of reducibility and of choice (for all types) ((K Godel , On formally undecidable propositions of principia mathematica and related

20. Set Theory/Zorn's Lemma And The Axiom Of Choice - Wikibooks, Collection Of Open-
That is, given Zorn s Lemma, one can derive the Axiom of choice and vice versa. certain propositions P logically equivalent to Zorn s Lemma (over ZF).
http://en.wikibooks.org/wiki/Set_Theory/Zorn's_Lemma_and_the_Axiom_of_Choice

21. A New Kind Of Science: The NKS Forum - 5 Reasons Why Godels Incompleteness Theor
and the axioms of reducibility and of choice (for all types) (K Godel , On formally undecidable propositions of principia mathematica and related systems

22. Intute: Science, Engineering And Technology - Browse Set Theory
The page includes links to the key people involved in the development of the theory, as well as to links to related areas such as the Axiom of choice and
http://www.intute.ac.uk/sciences/cgi-bin/browse.pl?id=27000

23. Math History - 20th Century ...
1963, Cohen proves the independence of the Axiom of choice and of the continuum approximately 4.669201660910 , which is related to perioddoubling
http://lahabra.seniorhigh.net/PAGES/teachers/pages/math/timeline/m20thCentury.ht

24. Axiom Of Choice - Quotes
Translate this page A selection of articles related to Axiom of choice - Quotes. To see this, for any proposition let be the set and let be the set (see Set-builder
http://www.experiencefestival.com/axiom_of_choice_-_quotes

25. JSTOR A Mathematical Axiom Contradicting The Axiom Of Choice.
The Axiom of determinateness is the proposition ~. It is observed that although the Axiom of choice and the Axiom of determinateness are inconsistent,

26. The Computer Journal -- Sign In Page
There is therefore a need to investigate how the constructive Axiom of choice, validated by the BrouwerHeyting-Kolmogorov interpretation, is related to
http://comjnl.oxfordjournals.org/cgi/content/full/49/3/345

27. Kurt Gödel, Or Kurt Goedel (American Mathematician) -- Britannica Online En
influence on Turing, algorithms, Axiom of choice, Axiomatization, mathematical system there are propositions (or questions) that cannot be proved or
http://www.britannica.com/eb/topic-236770/Kurt-Godel

28. The Axiom Of Choice And Non-enumerable Reals
Proposition The ZermeloFraenkel power set Axiom and the Axiom of choice are inconsistent if an extended language is not used to express all the reals.
http://www.angelfire.com/az3/nfold/choice.html

29. Peter Suber, "Kurt Gödel In Blue Hill"
Gödel s 1938 proof provided the related result that the negation of the Axiom of choice could not be derived from the standard Axioms.
http://www.earlham.edu/~peters/writing/godel.htm

30. The Axiom Of Choice Is Wrong « The Everything Seminar
The argument against the Axiom of choice which really hit a chord I first .. form opinions on the right choices for various undecidable propositions
http://cornellmath.wordpress.com/2007/09/13/the-axiom-of-choice-is-wrong/

31. Fuzzy Logic
These propositions are undecidable within ZFC, in some sense they are Goedel sentences . 3. If the Axiom of choice proposition is true then in ZFC there

32. Brunner: Positive Functionals And The Axiom Of Choice
Positive functionals and the Axiom of choice NorbertBrunner In this note we prove, that a proposition which is useful in integration theory, is equivalent
http://www.numdam.org/numdam-bin/fitem?id=RSMUP_1984__72__9_0

33. Programming And Computation
The proposition is the statement of the Law of Excluded Middle, . The Axiom of choice may also be viewed as an assertion that set s membership predicate
http://okmij.org/ftp/Computation/

34. Gödel
One of the most amazing Axioms in all of mathematics is The Axiom of choice. It basically says that many mathematical propositions can only be proved
http://www.yhwh.com/Thoughts/godel.htm

35. Math Forum - Math Library - Publications & Logic/Foundations & Research
This assertion is easy to prove using the Axiom of choice, but becomes a much . This site presents a set theory description of the proposition and an
http://mathforum.org/library/results.html?ed_topics=&levels=research&resource_ty

36. Practical Foundations Of Mathematics
His 1904 proof of the wellordering principle (Proposition 6.7.13 and Exercise 6.53) attracted DEFINITION 1.8.9 The Axiom of dependent choice says that
http://www.cs.man.ac.uk/~pt/Practical_Foundations/html/s18.html

37. The Googol Room
Group theorys adaptation to temporal propositions will be a more subtle matter than . It also abandons the Axiom of choice (AOC) as a practical matter.
http://www.googolroom.org/GrailMachineTwo.htm

38. The Ithaca Papers
Can this be done when the propositions of a mere philosophical perspective . the Axiom of choice or propositional calculi with morders of logical-value.
http://www.geocities.com/moonhoabinh/ithapapers/econo.html

39. Russell's Paradox (Stanford Encyclopedia Of Philosophy)
For example, assuming both P and ~P, any arbitrary proposition, Q, can be proved as follows ZF and ZFC (i.e., ZF supplemented by the Axiom of choice),

40. 20th WCP: Do Sentences Have Identity?
Some logicians have rejected propositions in favour of sentences, . Zermelos Axiom of choice (AC) is logically equivalent to Zorns lemma (ZL),
http://www.bu.edu/wcp/Papers/Logi/LogiBeza.htm

41. AMERICAN MATHEMATICAL MONTHLY - June/July 2001
Two Classical Surprises Concerning the Axiom of choice and the Continuum Hypothesis (Trichotomy is the proposition that of any two cardinals, a and b,
http://www.maa.org/pubs/monthly_jj02_toc.html

42. Springer Online Reference Works
a) the Axiom of choice and the generalized continuum hypothesis are has made it possible to state a proposition on the unsolvability in principal (in an
http://eom.springer.de/A/a014310.htm

43. An Encoding Of Zermelo-Fraenkel Set Theory In Coq
A noncomputational type-theoretical Axiom of choice is necessary to prove the Aczel s is that propositions are defined on the impredicative level Prop.
http://coq.inria.fr/contribs/zermelo-fraenkel.html

44. Axiom Of Choice - Wikipedia, The Free Encyclopedia
As this could be done for any proposition, this completes the proof that the Axiom of choice implies the law of the excluded middle. Forms of the Axiom of
http://en.wikipedia.org/wiki/Axiom_of_choice

45. FP Lunch
It is strange on the one hand the Axiom of choice is singled out as the I showed that while the proofrelevant Axiom of choice is provable in Type
http://sneezy.cs.nott.ac.uk/fplunch/weblog/

46. School Of Mathematics
The most interesting feature of set theory is the Axiom of choice one (The proposition that every injective function has a left inverse is much weaker.
http://www.maths.tcd.ie/pub/official/Courses04-05/371.html

47. Untitled Page
By the Axiom of choice, we can assume that P is wellordered. If n is not a point then let P be the first proposition in the well-ordering which is not
http://www.ihmc.us/users/phayes/context/ContextMereology.html

48. Axiom - Wiktionary
(philosophy) A selfevident and necessary truth; a proposition which it is The axioms of political economy cannot be considered absolute truths.
http://en.wiktionary.org/wiki/axiom

49. The Accursed Share: Sets & Numbers & Physics - Oh My!
Anyways, what Badiou seems to mean by his proposition is that mathematics (specifically, ZermeloFraenkel set theory, with the Axiom of choice,
http://accursedshare.blogspot.com/2006/02/sets-numbers-physics-oh-my.html

50. Equivalent To Axiom Of Choice? - Sci.math.research | Google Groups
the Axiom of choice. To be sure, the Hausdorff maximal principle states that any totally It is undesirable to believe a proposition