منابع مشابه
The Axiom of Choice
We propose that failures of the axiom of choice, that is, surjective functions admitting no sections, can be reasonably classified by means of invariants borrowed from algebraic topology. We show that cohomology, when defined so that its usual exactness properties hold even in the absence of the axiom of choice, is adequate for detecting failures of this axiom in the following sense. If a set X...
متن کاملThe Axiom of Choice
We propose that failures of the axiom of choice, that is, surjective functions admitting no sections, can be reasonably classified by means of invariants borrowed from algebraic topology. We show that cohomology, when defined so that its usual exactness properties hold even in the absence of the axiom of choice, is adequate for detecting failures of this axiom in the following sense. If a set X...
متن کاملEquivalents of the axiom of choice
Parts of this note have been discussed elsewhere in the blog, sometimes in a different form (see here and here, for example), but I haven’t examined before the equivalence of 5–7 with choice. In the course of the proof of the equivalence of item 7 with the other statements, a few additional equivalent versions of independent interest will be identified. The equivalence of 1–3 is classic. Zermel...
متن کاملUnions and the axiom of choice
Omar De la Cruz∗1, Eric J. Hall∗∗2, Paul Howard∗∗∗3, Kyriakos Keremedis†4, and Jean E. Rubin 1 Department of Statistics, University of Chicago, 5734 S. University Avenue, Chicago, IL 60637, USA 2 Department of Mathematics and Statistics, University of Missouri, Kansas City, MO 64110, USA 3 Department of Mathematics, Eastern Michigan University, Ypsilanti, MI 48197, USA 4 Department of Mathemati...
متن کاملDecision and Choice: Luce’s Choice Axiom
Luce’s choice axiom (LCA) is a theory of individual choice behavior that has proven to be a powerful tool in the behavioral sciences for over 50 years. LCA is grounded in two fundamental properties: choice is probabilistic and the probability of choosing an option from one set of alternatives is related to the probability of choosing the same option from a different set. This entry reviews the ...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1980
ISSN: 0022-4049
DOI: 10.1016/0022-4049(80)90097-3