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Oct 27, 2023 at 14:59 comment added Gabe Goldberg 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!
Oct 27, 2023 at 5:01 comment added Monroe Eskew Thanks for your answer. Could you say a bit about the consistency proof for the class of indestructibly sigma2 correct cardinals?
Oct 27, 2023 at 4:26 vote accept Monroe Eskew
Oct 26, 2023 at 20:51 history answered Gabe Goldberg CC BY-SA 4.0