Non-Galvin filters

Tom Benhamou; Shimon Garti; Moti Gitik; Alejandro Poveda

doi:10.1142/s021906132450017x

Non-Galvin filters

Tom Benhamou
, Shimon Garti
, Moti Gitik
, Alejandro Poveda^*

^*Corresponding author for this work

Einstein Institute of Mathematics

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

2 Scopus citations

Abstract

We address the question of consistency strength of certain filters and ultrafilters which fail to satisfy the Galvin property. We answer questions [Benhamou and Gitik, Ann. Pure Appl. Logic 173 (2022) 103107; Questions 7.8, 7.9], [Benhamou et al., J. Lond. Math. Soc. 108(1) (2023) 190-237; Question 5] and improve theorem [Benhamou et al., J. Lond. Math. Soc. 108(1) (2023) 190-237; Theorem 2.3].

Original language	English
Article number	2450017
Journal	Journal of Mathematical Logic
Volume	25
Issue number	2
DOIs	https://doi.org/10.1142/s021906132450017x
State	Published - 1 Aug 2025

Bibliographical note

Publisher Copyright:
© 2025 World Scientific Publishing Company.

Keywords

Galvin's property
Prikry-type forcings
singular cardinals

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10.1142/s021906132450017x

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abstract = "We address the question of consistency strength of certain filters and ultrafilters which fail to satisfy the Galvin property. We answer questions [Benhamou and Gitik, Ann. Pure Appl. Logic 173 (2022) 103107; Questions 7.8, 7.9], [Benhamou et al., J. Lond. Math. Soc. 108(1) (2023) 190-237; Question 5] and improve theorem [Benhamou et al., J. Lond. Math. Soc. 108(1) (2023) 190-237; Theorem 2.3].",

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AU - Gitik, Moti

AU - Poveda, Alejandro

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N2 - We address the question of consistency strength of certain filters and ultrafilters which fail to satisfy the Galvin property. We answer questions [Benhamou and Gitik, Ann. Pure Appl. Logic 173 (2022) 103107; Questions 7.8, 7.9], [Benhamou et al., J. Lond. Math. Soc. 108(1) (2023) 190-237; Question 5] and improve theorem [Benhamou et al., J. Lond. Math. Soc. 108(1) (2023) 190-237; Theorem 2.3].

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KW - Prikry-type forcings

KW - singular cardinals

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Non-Galvin filters

Abstract

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Keywords

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