An equiconsistency for universal indestructibility

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Journal of Symbolic Logic 75 (1):314-322 (2010)
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Abstract

We obtain an equiconsistency for a weak form of universal indestructibility for strongness. The equiconsistency is relative to a cardinal weaker in consistency strength than a Woodin cardinal. Stewart Baldwin's notion of hyperstrong cardinal. We also briefly indicate how our methods are applicable to universal indestructibility for supercompactness and strong compactness

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10.2178/jsl/1264433923

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Citations of this work

Indestructible Strong Unfoldability.Joel David Hamkins & Thomas A. Johnstone - 2010 - Notre Dame Journal of Formal Logic 51 (3):291-321.
The large cardinals between supercompact and almost-huge.Norman Lewis Perlmutter - 2015 - Archive for Mathematical Logic 54 (3-4):257-289.
Weak Indestructibility and Reflection.James Holland - forthcoming - Journal of Symbolic Logic:1-27.
Indestructibility of Vopěnka’s Principle.Andrew D. Brooke-Taylor - 2011 - Archive for Mathematical Logic 50 (5-6):515-529.

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References found in this work

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Gap forcing: Generalizing the lévy-Solovay theorem.Joel David Hamkins - 1999 - Bulletin of Symbolic Logic 5 (2):264-272.

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