Baire spaces and infinite games

Fred Galvin, Marion Scheepers

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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.

Original languageEnglish
Pages (from-to)85-104
Number of pages20
JournalArchive for Mathematical Logic
Volume55
Issue number1-2
DOIs
StatePublished - 1 Feb 2016

Keywords

  • Baire space
  • Infinite game
  • Measurable cardinal

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