The baire category theorem and cardinals of countable cofinality

Journal of Symbolic Logic 47 (2):275-288 (1982)
Abstract
Let κ B be the least cardinal for which the Baire category theorem fails for the real line R. Thus κ B is the least κ such that the real line can be covered by κ many nowhere dense sets. It is shown that κ B cannot have countable cofinality. On the other hand it is consistent that the corresponding cardinal for 2 ω 1 be ℵ ω . Similar questions are considered for the ideal of measure zero sets, other ω 1 saturated ideals, and the ideal of zero-dimensional subsets of R ω 1
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DOI 10.2307/2273142
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Internal Cohen Extensions.D. A. Martin & R. M. Solovay - 1970 - Annals of Mathematical Logic 2 (2):143-178.

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Game Ideals.Pierre Matet - 2009 - Annals of Pure and Applied Logic 158 (1):23-39.

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