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Combinatorics of ultrafilters on Cohen and random algebras

We investigate the structure of ultrafilters on Boolean algebras in the framework of Tukey reducibility. In particular, this paper provides several techniques to construct ultrafilters which are not Tukey maximal. Furthermore, we connect this analysis with a cardinal invariant of Boolean algebras, the ultrafilter number, and prove consistency results concerning its possible values on Cohen and random algebras.

preprint2021arXivOpen access
Jörg BrendleFrancesco Parente
math.LO
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Jörg BrendleFrancesco Parente

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