TL;DR
This paper introduces Magidor cardinals, a variation of J46nsson cardinals involving colorings of countably bounded subsets, and explores their consistency with large cardinals.
Contribution
It defines Magidor cardinals and proves their non-existence is consistent alongside large cardinal assumptions.
Findings
Magidor cardinals are a new variation of J46nsson cardinals.
It is consistent that large cardinals exist without Magidor cardinals.
The paper establishes the independence of Magidor cardinals from large cardinal axioms.
Abstract
We define Magidor cardinals as J\'onsson cardinals upon replacing colorings of finite subsets by colorings of -bounded subsets. Unlike J\'onsson cardinals which appear at some low level of large cardinals, we prove the consistency of having quite large cardinals along with the fact that no Magidor cardinal exists.
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