A parametrized diamond principle and union ultrafilters

David Fernández-Bretón; Michael Hrušák

doi:10.4064/cm7364-10-2017

A parametrized diamond principle and union ultrafilters

David Fernández-Bretón, Michael Hrušák

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

4 Scopus citations

Abstract

We consider a cardinal invariant closely related to Hindman’s theorem. We prove that this invariant is small in the iterated Sacks perfect set forcing model, and its corresponding parametrized diamond principle implies the existence of union ultrafilters. As a corollary, we obtain the existence of union ultrafilters in the iterated Sacks model of set theory.

Original language	English
Pages (from-to)	261-272
Number of pages	12
Journal	Colloquium Mathematicum
Volume	153
Issue number	2
DOIs	https://doi.org/10.4064/cm7364-10-2017
State	Published - 2018
Externally published	Yes

Keywords

Cardinal invariants of the continuum
Hindman’s theorem
Iterated Sacks model
Iterated perfect set forcing
Parametrized diamond principles
Union ultrafilters

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N2 - We consider a cardinal invariant closely related to Hindman’s theorem. We prove that this invariant is small in the iterated Sacks perfect set forcing model, and its corresponding parametrized diamond principle implies the existence of union ultrafilters. As a corollary, we obtain the existence of union ultrafilters in the iterated Sacks model of set theory.

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KW - Cardinal invariants of the continuum

KW - Hindman’s theorem

KW - Iterated Sacks model

KW - Iterated perfect set forcing

KW - Parametrized diamond principles

KW - Union ultrafilters

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A parametrized diamond principle and union ultrafilters

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Keywords

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