Article
Baire Spaces and Infinite Games
Archive for Mathematical Logic
Document Type
Article
Publication Date
2-1-2016
Disciplines
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.
Citation Information
Fred Galvin and Marion Scheepers. "Baire Spaces and Infinite Games" Archive for Mathematical Logic (2016) Available at: http://works.bepress.com/marion_scheepers/23/