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arXiv · 2012.02306

The ultrafilter and almost disjointness numbers

Osvaldo Guzman·Damjan Kalajdzievski
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Abstract

We prove that every MAD family can be destroyed by a proper forcing that preserves $P$-points. With this result, we prove that it is consistent that $\omega_{1}=\mathfrak{u}<\mathfrak{a,}$ solving a nearly 20 year old problem of Shelah and a problem of Brendle. We will also present a simple proof of a result of Blass and Shelah that the inequality $\mathfrak{u<s}$ is consistent.

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Osvaldo Guzman, Damjan Kalajdzievski. 2020-12-03. The ultrafilter and almost disjointness numbers. https://arxiv.org/abs/2012.02306

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