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The Baire category theorem and cardinals of countable cofinality

Published online by Cambridge University Press:  12 March 2014

Arnold W. Miller
Arnold W. Miller*
Affiliation:
University of Wisconsin, Madison, Wisconsin 53706 University of Texas, Austin, Texas 76712
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Abstract

Let κB be the least cardinal for which the Baire category theorem fails for the real line R. Thus κB is the least κ such that the real line can be covered by κ many nowhere dense sets. It is shown that κB cannot have countable cofinality. On the other hand it is consistent that the corresponding cardinal for 2ω1 be ℵω. Similar questions are considered for the ideal of measure zero sets, other ω1, saturated ideals, and the ideal of zero-dimensional subsets of Rω1.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 47 , Issue 2 , June 1982 , pp. 275 - 288
Copyright
Copyright © Association for Symbolic Logic 1982

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