English

Jonsson and Magidor filters

Logic 2025-03-19 v1

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.

Cite

@article{arxiv.2503.13744,
  title  = {Jonsson and Magidor filters},
  author = {Omer Ben-Neria and Shimon Garti},
  journal= {arXiv preprint arXiv:2503.13744},
  year   = {2025}
}
R2 v1 2026-06-28T22:24:30.045Z