A simple formula equivalent to the axiom of choice.
نویسندگان
چکیده
منابع مشابه
Some Restricted Lindenbaum Theorems Equivalent to the Axiom of Choice
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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...
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ژورنال
عنوان ژورنال: Notre Dame Journal of Formal Logic
سال: 1960
ISSN: 0029-4527
DOI: 10.1305/ndjfl/1093956553