Notre Dame Journal of Formal Logic

Powers of 2

Horst Herrlich and Kyriakos Keremedis

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 2X 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.

Article information

Source
Notre Dame J. Formal Logic, Volume 40, Number 3 (1999), 346-351.

Dates
First available in Project Euclid: 28 May 2002

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1022615615

Digital Object Identifier
doi:10.1305/ndjfl/1022615615

Mathematical Reviews number (MathSciNet)
MR1845626

Zentralblatt MATH identifier
1058.03050

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

Citation

Keremedis, Kyriakos; Herrlich, Horst. Powers of 2. Notre Dame J. Formal Logic 40 (1999), no. 3, 346--351. doi:10.1305/ndjfl/1022615615. https://projecteuclid.org/euclid.ndjfl/1022615615


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References

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