Jonsson and Magidor filters

We study the filter versions of square bracket partition relations, focusing on Jonssonicity and Magidority. We show that the singular cardinals in a Kleinberg sequence above some strong partition cardinal are not Magidor, but the limit of the sequence is Magidor. This is done under AD. We also force over a model of AD to obtain a singular cardinal carrying a Magidor filter.

Publication Details

Journal
ArXiv.org
Published
2025-03-17
Primary Topic
Advanced Topology and Set Theory
Type
article
Field-Weighted Citation Impact
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article

Jonsson and Magidor filters

ArXiv.org
Advanced Topology and Set Theory
article

Jonsson and Magidor filters

article en

Abstract

We study the filter versions of square bracket partition relations, focusing on Jonssonicity and Magidority. We show that the singular cardinals in a Kleinberg sequence above some strong partition cardinal are not Magidor, but the limit of the sequence is Magidor. This is done under AD. We also force over a model of AD to obtain a singular cardinal carrying a Magidor filter.

ArXiv.org
Reduced inequalities
Openalex Percentile: Top 44%
Advanced Topology and Set Theory
Open Access PDFOpenAlex
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Jonsson and Magidor filters · ArXiv.org (2025) | TGRS Research Map | TGRS