Baire Spaces and Infinite Games

Fred Galvin; Marion Scheepers

doi:10.1007/s00153-015-0461-8

Baire Spaces and Infinite Games

Fred Galvin
, Marion Scheepers

Mathematics Department

University of Kansas

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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
Pages (from-to)	85-104
Number of pages	20
Journal	Archive for Mathematical Logic
Volume	55
Issue number	1-2
DOIs	https://doi.org/10.1007/s00153-015-0461-8
State	Published - Feb 2016

Keywords

Baire space
Infinite game
Measurable cardinal

EGS Disciplines

Mathematics

Access to Document

10.1007/s00153-015-0461-8

Cite this

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title = "Baire Spaces and Infinite Games",

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.",

keywords = "Baire space, Infinite game, Measurable cardinal",

author = "Fred Galvin and Marion Scheepers",

note = "Publisher Copyright: {\textcopyright} 2015, Springer-Verlag Berlin Heidelberg.",

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language = "American English",

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AU - Scheepers, Marion

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N2 - 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.

AB - 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.

KW - Baire space

KW - Infinite game

KW - Measurable cardinal

UR - https://www.scopus.com/pages/publications/84956607044

UR - https://scholarworks.boisestate.edu/math_facpubs/178

U2 - 10.1007/s00153-015-0461-8

DO - 10.1007/s00153-015-0461-8

M3 - Article

SN - 0933-5846

VL - 55

SP - 85

EP - 104

JO - Archive for Mathematical Logic

JF - Archive for Mathematical Logic

IS - 1-2

ER -

Baire Spaces and Infinite Games

Abstract

Keywords

EGS Disciplines

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