2014/01/23 by Galvin, Fred, Scheepers, Marion
#03E55 #03E60 #03E65 #54B10 #54E52 #91A44 #91A46 #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO)
paper · doi:10.48550/arxiv.1401.6061
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 topology. The converse of this implication may be true also: 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.