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 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 ...
متن کاملFraenkel’s axiom of restriction: Axiom choice, intended models and categoricity
A recent debate has focused on different methodological principles underlying the practice of axiom choice in mathematics (cf. Feferman et al., 2000; Maddy, 1997; Easwaran, 2008). The general aim of these contributions can be described as twofold: first to clarify the spectrum of informal justification strategies retraceable in the history of mathematical axiomatics. Second, to evaluate and to ...
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...
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ژورنال
عنوان ژورنال: Mathematica Moravica
سال: 2004
ISSN: 1450-5932,2560-5542
DOI: 10.5937/matmor0401039t