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Axiom of Choice
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41	Mechanizing Set Theory Cardinal Arithmetic and the Axiom of Choice Lawrence C. Paulson Computer Laboratory, University of Cambridge email: [removed] Add to Reading List Source URL: www.cl.cam.ac.uk Language: English - Date: 2003-04-29 07:49:46 Cardinal numbers Large cardinals Set theory Axiom of choice Zermelo–Fraenkel set theory Constructible universe First-order logic Mathematical proof Successor cardinal Mathematical logic Mathematics Logic
42	Applications of inductive definitions and choice principles to program synthesis Ulrich Berger and Monika Seisenberger {u.berger,csmona}@swansea.ac.uk University of Wales Swansea Add to Reading List Source URL: www-compsci.swan.ac.uk Language: English - Date: 2006-06-27 17:59:13 Structural induction Mathematical proof Mathematical induction Well-quasi-ordering Axiom of choice Recursion Intuitionistic type theory Well-founded relation Bar induction Mathematics Mathematical logic Logic
43	A New System of Axioms Instead of ZF (ver[removed]Use a Latin font such as Times New Roman, please.] [If not word-wrapped, see "Word-wrap" of HELP in your software.] Add to Reading List Source URL: hp.vector.co.jp Language: English - Date: 2004-09-05 11:07:18 Axioms of set theory Z notation Urelements Zermelo–Fraenkel set theory Constructible universe Axiom of choice First-order logic Axiom Function Mathematical logic Logic Mathematics
44	Annals of the Japan Association for Philosophy of Science Vol[removed] Add to Reading List Source URL: math.bu.edu Language: English - Date: 2012-03-06 14:12:29 Cardinal numbers Infinity Set theory Formal systems Real number Georg Cantor Axiom of choice Uncountable set Continuum hypothesis Mathematics Mathematical logic Logic
45	Descriptive Set Theory, Equivalence Relations, and Classification Problems in Analysis by Add to Reading List Source URL: www.its.caltech.edu Language: English - Date: 2001-09-29 05:40:26 Descriptive set theory Borel set Borel equivalence relation Wadge hierarchy Space Metric space Axiom of choice Polish space Equivalence relation Mathematical logic Set theory Mathematics
46	Tutorial on Axiomatic Set Theory Javier R. Movellan Add to Reading List Source URL: mplab.ucsd.edu Language: English - Date: 2007-07-19 19:21:57 Z notation Axioms of set theory Function Zermelo–Fraenkel set theory First-order logic Constructible universe Axiom of choice Axiom Universal quantification Mathematical logic Logic Mathematics
47	DEFINITIONS OF FINITENESS BASED ON ORDER PROPERTIES OMAR DE LA CRUZ, DAMIR D. DZHAFAROV, AND ERIC J. HALL Add to Reading List Source URL: h.web.umkc.edu Language: English - Date: 2005-10-03 16:55:57 Dedekind-infinite set Axiom of choice Order theory Locally finite collection Amorphous set Mathematics Cardinal numbers Finite set
48	The Well-Ordering Theorem one of the Greatest Mathematical Controversies of All Time Recall that the set of natural numbers with the order < is well-ordered. In general, a Add to Reading List Source URL: math.uchicago.edu Language: English - Date: 2011-10-20 18:46:28 Z notation Set theory Axiom of choice Well-ordering theorem Well-order Ernst Zermelo Real number Axiom S Mathematical logic Mathematics Logic
49	1506 MATHEMATICS: F. W. LAWVERE Add to Reading List Source URL: www.pnas.org Language: English - Date: 2005-04-22 15:00:13 Homological algebra Algebraic topology Sheaf Peano axioms Axiom of choice Function Injective function Adjoint functors Isomorphism Mathematics Mathematical logic Functions and mappings
50	Two Classical Surprises Concerning the Axiom of Choice and the Continuum Hypothesis Add to Reading List Source URL: www.maa.org Language: English - Date: 2013-07-12 13:40:31 Cardinal numbers Infinity Ordinal numbers Forcing Axiom of choice Zermelo–Fraenkel set theory Transfinite number Continuum hypothesis Constructible universe Mathematical logic Mathematics Set theory

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