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COMBINATORICS OF ULTRAFILTERS ON COHEN AND RANDOM ALGEBRAS
Published online by Cambridge University Press: 15 February 2021
Abstract
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.
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- © The Author(s), 2021. Published by Cambridge University Press on behalf of The Association for Symbolic Logic
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