Archive for Mathematical Logic

, Volume 55, Issue 1–2, pp 85–104 | Cite as

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 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.


Baire space Infinite game Measurable cardinal 

Mathematics Subject Classification

03E55 03E60 03E65 54B10 54E52 91A44 91A46 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of KansasLawrenceUSA
  2. 2.Department of MathematicsBoise State UniversityBoiseUSA

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