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Baire spaces and infinite games

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.

preprint2014arXivOpen access
Fred GalvinMarion Scheepers
math.GNmath.LO
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Fred GalvinMarion Scheepers

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