Baire spaces and infinite games

被引：1

作者：

Galvin, Fred ^{[1
]}

Scheepers, Marion ^{[2
]}

机构：

[1] Univ Kansas, Dept Math, Lawrence, KS 66045 USA

[2] Boise State Univ, Dept Math, Boise, ID 83725 USA

来源：

ARCHIVE FOR MATHEMATICAL LOGIC | 2016年 / 55卷 / 1-2期

关键词：

Baire space; Infinite game; Measurable cardinal;

D O I：

10.1007/s00153-015-0461-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：85 / 104

页数：20

共 10 条

[1]

[Anonymous], 1981, The Scottish Book: Mathematics from the Scottish Cafe

[2]

[Anonymous], ANN MATH STUD

[3] IDEAL GAME [J].