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 language | English |
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Pages (from-to) | 85-104 |
Number of pages | 20 |
Journal | Archive for Mathematical Logic |
Volume | 55 |
Issue number | 1-2 |
DOIs | |
State | Published - 1 Feb 2016 |
Keywords
- Baire space
- Infinite game
- Measurable cardinal