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Powers of 2. (English) Zbl 1058.03050
Summary: It is shown that, in ZF, Martin’s $$\aleph_{0}^{}$$-axiom together with the axiom of countable choice for finite sets imply that arbitrary powers $$2^X$$ of a 2-point discrete space are Baire and that the latter property implies the following: (a) the axiom of countable choice for finite sets, (b) power sets of infinite sets are Dedekind-infinite, (c) there are no amorphous sets, and (d) weak forms of the Kinna-Wagner principle.

MSC:
 3e+25 Axiom of choice and related propositions 5.4e+53 Baire category, Baire spaces
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References:
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