Baire Category for Monotone Sets

Andreas Blass

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arXiv · math/9405203

Baire Category for Monotone Sets

Andreas Blass

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Abstract

We study Baire category for subsets of 2^omega that are downward-closed with respect to the almost-inclusion ordering (on the power set of the natural numbers, identified with 2^omega). We show that it behaves better in this context than for general subsets of 2^omega. In the downward-closed context, the ideal of meager sets is prime and b-complete (where b is the bounding number), while the complementary filter is g-complete (where g is the groupwise density cardinal). We also discuss other cardinal characteristics of this ideal and this filter, and we show that analogous results for measure in place of category are not provable in ZFC.

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BibTeX RIS

Andreas Blass. 1994-05-20. Baire Category for Monotone Sets. https://arxiv.org/abs/math/9405203

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