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Some weak forms of the Baire category theorem
Author(s) -
Kermedis Kyriakos
Publication year - 2003
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200310039
Subject(s) - mathematics , baire category theorem , axiom of choice , separable space , countable set , axiom , statement (logic) , baire measure , baire space , real line , pure mathematics , zermelo–fraenkel set theory , discrete mathematics , set (abstract data type) , set theory , mathematical analysis , geometry , computer science , political science , law , programming language
Abstract We show that the statement (K12) “separable, countably compact, regular spaces are Baire” is deducible from a strictly weaker form than AC, namely, CAC(ℝ) (the axiom of choice for countable families of non‐empty subsets of the real line ℝ). We also find some characterizations of the axiom of dependent choices.