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$\begingroup$ Thanks for your answer. Could you say a bit about the consistency proof for the class of indestructibly sigma2 correct cardinals? $\endgroup$
– Monroe Eskew
Commented Oct 27, 2023 at 5:01
1

$\begingroup$ The proof assuming a proper class of inaccessible $\Sigma_2$-reflecting cardinals (which follows from Ord is Mahlo) is in my paper "On Usuba's extendible cardinal," which is on the arXiv. In a more recent version of the paper, the assumption is reduced to just ZFC, but I'm still working on the presentation. I actually made every $\Sigma_2$-reflecting cardinal indestructible! $\endgroup$
– Gabe Goldberg
Commented Oct 27, 2023 at 14:59

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