Non-Galvin Filters
Tom Benhamou, Shimon Garti, Moti Gitik, Alejandro Poveda
TL;DR
This paper investigates the consistency strength of specific filters and ultrafilters that do not satisfy the Galvin property, providing new answers to existing questions and improving known theorems in the area.
Contribution
It offers new results on the consistency strength of non-Galvin filters and ultrafilters, addressing open questions and enhancing previous theorems.
Findings
Answered open questions about non-Galvin filters.
Improved theorems related to the consistency strength of certain filters.
Provided new insights into the structure of ultrafilters failing the Galvin property.
Abstract
We address the question of the consistency strength of certain filters and ultrafilters which fail to satisfy the Galvin property. We answer questions \cite[Questions 7.8,7.9]{TomMotiII}, \cite[Question 5]{NegGalSing} and improve theorem \cite[Theorem 2.3]{NegGalSing}.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Mathematical Analysis and Transform Methods · Algebraic structures and combinatorial models