Easton's theorem in the presence of Woodin cardinals

DOI10.1007/S00153-013-0332-0zbMATH Open1305.03039arXiv1207.5822OpenAlexW2087110253MaRDI QIDQ365667

Brent M. Cody

Publication date: 9 September 2013

Published in: Archive for Mathematical Logic (Search for Journal in Brave)

Abstract: Under the assumption that $delta$ is a Woodin cardinal and $GCH$ holds, I show that if $F$ is any class function from the regular cardinals to the cardinals such that (1) $kappa<cf(F(kappa))$, (2) $kappa<lambda$ implies $F(kappa)leqF(lambda)$, and (3) $delta$ is closed under $F$, then there is a cofinality-preserving forcing extension in which $2^{g}amma=F(gamma)$ for each regular cardinal $gamma<delta$, and in which $delta$ remains Woodin. Unlike the analogous results for supercompact cardinals [Men76] and strong cardinals [FH08], there is no requirement that the function $F$ be locally definable.

Full work available at URL: https://arxiv.org/abs/1207.5822

zbMATH Keywords

continuum functionEaston's theoremWoodin cardinals

Mathematics Subject Classification ID

Consistency and independence results (03E35) Large cardinals (03E55)

Cites Work

• Title not available (Why is that?)
• On supercompactness and the continuum function
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• A Model in Which GCH Holds at Successors but Fails at Limits
• Consistency Results Concerning Supercompactness
• Canonical seeds and Prikry trees
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• An Easton theorem for level by level equivalence
• Powers of regular cardinals

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WOODIN FOR STRONG COMPACTNESS CARDINALS ⋮ Easton's theorem and large cardinals ⋮ Large cardinals need not be large in HOD ⋮ An Easton like theorem in the presence of Shelah cardinals ⋮ Forcing many positive polarized partition relations between a cardinal and its powerset ⋮ Easton's theorem for the tree property below \(\aleph_\omega\)

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