A small ultrafilter number at smaller cardinals

Dilip Raghavan; Saharon Shelah

doi:10.1007/s00153-019-00693-8

A small ultrafilter number at smaller cardinals

Dilip Raghavan^*, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

It is proved to be consistent relative to a measurable cardinal that there is a uniform ultrafilter on the real numbers which is generated by fewer than the maximum possible number of sets. It is also shown to be consistent relative to a supercompact cardinal that there is a uniform ultrafilter on ℵ_ω ₊ ₁ which is generated by fewer than 2ℵω+1 sets.

Original language	English
Pages (from-to)	325-334
Number of pages	10
Journal	Archive for Mathematical Logic
Volume	59
Issue number	3-4
DOIs	https://doi.org/10.1007/s00153-019-00693-8
State	Published - 1 May 2020

Bibliographical note

Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.

Keywords

Cardinal invariant
Indecomposable ultrafilter
Large cardinal
Uniform ultrafilter

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10.1007/s00153-019-00693-8

Cite this

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A small ultrafilter number at smaller cardinals

Abstract

Bibliographical note

Keywords

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