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arXiv · 1401.6061

Baire spaces and infinite games

Fred Galvin·Marion Scheepers
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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 topology. The converse of this implication may be true also: 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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Fred Galvin, Marion Scheepers. 2014-10-24. Baire spaces and infinite games. https://arxiv.org/abs/1401.6061

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