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COMBINATORICS OF ULTRAFILTERS ON COHEN AND RANDOM ALGEBRAS

Part of: Ordered sets Set theory

Published online by Cambridge University Press:  15 February 2021

JÖRG BRENDLE  and
FRANCESCO PARENTE
JÖRG BRENDLE
Affiliation:
GRADUATE SCHOOL OF SYSTEM INFORMATICS KOBE UNIVERSITY 1-1 ROKKODAI-CHO NADA-KU KOBE, 657-8501, JAPANE-mail:brendle@kobe-u.ac.jpE-mail:parente@people.kobe-u.ac.jp
FRANCESCO PARENTE
Affiliation:
GRADUATE SCHOOL OF SYSTEM INFORMATICS KOBE UNIVERSITY 1-1 ROKKODAI-CHO NADA-KU KOBE, 657-8501, JAPANE-mail:brendle@kobe-u.ac.jpE-mail:parente@people.kobe-u.ac.jp
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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.

Keywords

ultrafilterBoolean algebraTukey reducibilitycardinal invariants

MSC classification

Primary: 03E05: Other combinatorial set theory
Secondary: 03E17: Cardinal characteristics of the continuum 06A07: Combinatorics of partially ordered sets 06E05: Structure theory
Type
Article
Information
The Journal of Symbolic Logic , Volume 87 , Issue 1 , March 2022 , pp. 109 - 126
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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