Another Equivalent form of the Axiom of Choice
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 ...
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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the present study investigated construct equivalence of multiple choice (mc) and constructed response (cr) item types across stem and content equivalent mc and cr items (item type ‘a’), non-stem-equivalent but content equivalent mc and cr items (item type ‘b’), and non-stem and non-content equivalent mc and cr items (item type ‘c’). one hundred seventy english-major undergraduates completed mc ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1966
ISSN: 0002-9939
DOI: 10.2307/2035083