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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.
Gabriel Goldberg (Fri,) studied this question.
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