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 | American English |
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Journal | Mathematics Faculty Publications and Presentations |
State | Published - 1 Feb 2016 |
Keywords
- 03E55
- 03E60
- 03E65
- baire space
- infinite game
- measurable cardinal
EGS Disciplines
- Mathematics