Powers of 2

Notre Dame Journal of Formal Logic 40 (3):346-351 (1999)
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It is shown that in ZF Martin's -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



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Citations of this work

MA(ℵ0) restricted to complete Boolean algebras and choice.Eleftherios Tachtsis - 2021 - Mathematical Logic Quarterly 67 (4):420-431.
On Martin's Axiom and Forms of Choice.Eleftherios Tachtsis - 2016 - Mathematical Logic Quarterly 62 (3):190-203.

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References found in this work

Provable forms of Martin's axiom.Gary P. Shannon - 1990 - Notre Dame Journal of Formal Logic 31 (3):382-388.
Consequences of the Axiom of Choice.Paul Howard & Jean E. Rubin - 2005 - Bulletin of Symbolic Logic 11 (1):61-63.
Sequential compactness and the axiom of choice.Norbert Brunner - 1983 - Notre Dame Journal of Formal Logic 24 (1):89-92.

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