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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:
03E25 Axiom of choice and related propositions
54E52 Baire category, Baire spaces
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