Usuba’s theorem is optimal

Journal of Mathematical Logic (forthcoming)
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Abstract

This paper answers a question of Usuba [Extendible cardinals and the mantle, Arch. Math. Logic 58(1–2) (2019) 71–75], establishing the optimality of the large cardinal assumption of his remarkable theorem that if there is an extendible cardinal, there is a minimum inner model from which the universe of sets can be obtained as a forcing extension.

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10.1142/s0219061324500259

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