Baire spaces and infinite games

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Archive for Mathematical Logic 55 (1-2):85-104 (2016)
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Abstract

It is well known that if the nonempty player of the Banach–Mazur game has a winning strategy on a space, then that space is Baire in all powers even in the box product topology. The converse of this implication may also be true: We know of no consistency result to the contrary. In this paper we establish the consistency of the converse relative to the consistency of the existence of a proper class of measurable cardinals.

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10.1007/s00153-015-0461-8

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References found in this work

[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
Set Theory.T. Jech - 2005 - Bulletin of Symbolic Logic 11 (2):243-245.
An ideal game.F. Galvin, T. Jech & M. Magidor - 1978 - Journal of Symbolic Logic 43 (2):284-292.
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