Powers of 2

Horst Herrlich; Kyriakos Keremedis

doi:10.1305/ndjfl/1022615615

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Home > Journals > Notre Dame J. Formal Logic > Volume 40 > Issue 3 > Article

Summer 1999 Powers of 2

Horst Herrlich, Kyriakos Keremedis

Notre Dame J. Formal Logic 40(3): 346-351 (Summer 1999). DOI: 10.1305/ndjfl/1022615615

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Abstract

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.