Tuesday, October 20, 2009

The Axiom of Choice

Three useful links dealing with the Axiom of Choice: The Axiom of Choice - Stanford Encyclopedia of Philosophy entry by John L. Bell, the University of Western Ontario; The Axiom of Choice (a short paper by Prof. John L. Bell) ; The Relative Consistency of the Axiom of Choice - Mechanized Using Isabelle/ZF by Lawrence C. Paulson, Computer Laboratory Univ. of Cambridge. An important result, in a categorical setting linked to intutionistic set theory, was obtained by Radu Diaconescu (Axiom of choice and complementation, Proc. Amer. Math. Soc. 51, 1975, 176-178): a topos satisfying the axiom of choice must be boolean (in short... the axiom of choice implies the law of the excluded middle).