Combinatorics of ultrafilters on Cohen and random algebras

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Journal of Symbolic Logic 87 (1):109-126 (2022)
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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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10.1017/jsl.2021.18

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References found in this work

Happy families.A. R. D. Mathias - 1977 - Annals of Mathematical Logic 12 (1):59.
Internal cohen extensions.D. A. Martin & R. M. Solovay - 1970 - Annals of Mathematical Logic 2 (2):143-178.
The fine structure of the constructible hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.
Konfinalität.Jürgen Schmidt - 1955 - Mathematical Logic Quarterly 1 (4):271-303.
Konfinalität.Jürgen Schmidt - 1955 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 1 (4):271-303.

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