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- W2052507977 abstract "Given a cardinal $kappa$ that is $lambda$-supercompact for some regular cardinal $lambdageqkappa$ and assuming $GCH$, we show that one can force the continuum function to agree with any function $F:[kappa,lambda]capREGtoCARD$ satisfying $forallalpha,betaindom(F)$ $alpha F(lambda)$. Our argument extends Woodin's technique of surgically modifying a generic filter to a new case: Woodin's key lemma applies when modifications are done on the range of $j$, whereas our argument uses a new key lemma to handle modifications done off of the range of $j$ on the ghost coordinates. This work answers a question of Friedman and Honzik [FH2012]. We also discuss several related open questions." @default.
- W2052507977 created "2016-06-24" @default.
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- W2052507977 date "2013-06-03" @default.
- W2052507977 modified "2023-09-27" @default.
- W2052507977 title "On supercompactness and the continuum function" @default.
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