An algebraic equivalent of a multiple choice axiom
نویسندگان
چکیده
منابع مشابه
Some Restricted Lindenbaum Theorems Equivalent to the Axiom of Choice
Dzik (1981) gives a direct proof of the axiom of choice from the generalized Lindenbaum extension theorem LET. The converse is part of every decent logical education. Inspection of Dzik’s proof shows that its premise let attributes a very special version of the Lindenbaum extension property to a very special class of deductive systems. The problem therefore arises of giving a direct proof, not ...
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Paracompactness of Metric Spaces and the Axiom of Multiple Choice
The axiom of multiple choice implies that metric spaces are paracompact but the reverse implication cannot be proved in set theory without the axiom of choice. 1. Background, Definitions and Summary of Results. Working in set theory without the axiom of choice we study the deductive strength of the assertion MP: Metric spaces are paracompact. (Definitions are given below.) MP was first proved i...
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 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: Fundamenta Mathematicae
سال: 1972
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-74-2-145-146