Notre Dame Journal of Formal Logic

Thin Ultrafilters

O. Petrenko and I. V. Protasov

Abstract

A free ultrafilter $\mathcal{U}$ on $\omega$ is called a $T$-point if, for every countable group $G$ of permutations of $\omega$, there exists $U\in\mathcal{U}$ such that, for each $g\in G$, the set $\{x\in U:gx\ne x, gx\in U\}$ is finite. We show that each $P$-point and each $Q$-point in $\omega^*$ is a $T$-point, and, under CH, construct a $T$-point, which is neither a $P$-point, nor a $Q$-point. A question whether $T$-points exist in ZFC is open.

Article information

Source
Notre Dame J. Formal Logic, Volume 53, Number 1 (2012), 79-88.

Dates
First available in Project Euclid: 9 May 2012

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1336586239

Digital Object Identifier
doi:10.1215/00294527-1626536

Mathematical Reviews number (MathSciNet)
MR2925270

Zentralblatt MATH identifier
1258.03057

Subjects
Primary: 54D35: Extensions of spaces (compactifications, supercompactifications, completions, etc.) 54D80: Special constructions of spaces (spaces of ultrafilters, etc.)

Keywords
ultrafilter thin set $P$-point $Q$-point $T$-point

Citation

Petrenko, O.; Protasov, I. V. Thin Ultrafilters. Notre Dame J. Formal Logic 53 (2012), no. 1, 79--88. doi:10.1215/00294527-1626536. https://projecteuclid.org/euclid.ndjfl/1336586239


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