Journal of Symbolic Logic

The Baire Category Theorem and Cardinals of Countable Cofinality

Arnold W. Miller

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Abstract

Let $\kappa_B$ be the least cardinal for which the Baire category theorem fails for the real line $\mathbf{R}$. Thus $\kappa_B$ is the least $\kappa$ such that the real line can be covered by $\kappa$ many nowhere dense sets. It is shown that $\kappa_B$ cannot have countable cofinality. On the other hand it is consistent that the corresponding cardinal for $2^{\omega_1}$ be $\aleph_\omega$. Similar questions are considered for the ideal of measure zero sets, other $\omega_1$ saturated ideals, and the ideal of zero-dimensional subsets of $\mathbf{R}^{\omega_1}$.

Article information

Source
J. Symbolic Logic, Volume 47, Issue 2 (1982), 275-288.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183740998

Mathematical Reviews number (MathSciNet)
MR654788

Zentralblatt MATH identifier
0487.03026

JSTOR
links.jstor.org

Citation

Miller, Arnold W. The Baire Category Theorem and Cardinals of Countable Cofinality. J. Symbolic Logic 47 (1982), no. 2, 275--288. https://projecteuclid.org/euclid.jsl/1183740998


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