Gruff ultrafilters

David J. Fernández-Bretón; Michael Hrušák

doi:10.1016/j.topol.2016.08.012

Gruff ultrafilters

David J. Fernández-Bretón, Michael Hrušák

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

1 Scopus citations

Abstract

We investigate the question of whether Q carries an ultrafilter generated by perfect sets (such ultrafilters were called gruff ultrafilters by van Douwen). We prove that one can (consistently) obtain an affirmative answer to this question in three different ways: by assuming a certain parametrized diamond principle, from the cardinal invariant equality d=c, and in the Random real model.

Original language	English
Pages (from-to)	355-365
Number of pages	11
Journal	Topology and its Applications
Volume	210
DOIs	https://doi.org/10.1016/j.topol.2016.08.012
State	Published - 1 Sep 2016
Externally published	Yes

Keywords

Dominating number
Parametrized diamond principle
Random forcing
Topology on the rationals
Ultrafilter

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10.1016/j.topol.2016.08.012

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abstract = "We investigate the question of whether Q carries an ultrafilter generated by perfect sets (such ultrafilters were called gruff ultrafilters by van Douwen). We prove that one can (consistently) obtain an affirmative answer to this question in three different ways: by assuming a certain parametrized diamond principle, from the cardinal invariant equality d=c, and in the Random real model.",

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KW - Parametrized diamond principle

KW - Random forcing

KW - Topology on the rationals

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Gruff ultrafilters

Abstract

Keywords

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