The first omitting cardinal for Magidority
Shimon Garti, Yair Hayut

TL;DR
This paper proves that the first omitting cardinal for Magidority can be a successor of a supercompact or singular cardinal, advancing understanding of large cardinal hierarchies and their relationships.
Contribution
It establishes the consistency of the first omitting cardinal for Magidority being a successor of a supercompact or singular cardinal, a novel result in large cardinal theory.
Findings
$oldsymbol{ ext{α}_M(oldsymbol{ ext{λ}})}$ can be a successor of a supercompact cardinal
$oldsymbol{ ext{α}_M(oldsymbol{ ext{λ}})}$ can be a successor of a singular cardinal with uncountable cofinality
Advances the understanding of the structure of Magidor cardinals and their associated omitting cardinals.
Abstract
We prove that can be successor of a supercompact cardinal, when is a Magidor cardinal. From this result we obtain the consistency of being a successor of a singular cardinal with uncountable cofinality.
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