Journal of Symbolic Logic

An equiconsistency for universal indestructibility

Arthur W. Apter and Grigor Sargsyan

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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.

Article information

J. Symbolic Logic, Volume 75, Issue 1 (2010), 314-322.

First available in Project Euclid: 25 January 2010

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03E35: Consistency and independence results 03E45: Inner models, including constructibility, ordinal definability, and core models 03E55: Large cardinals

Universal indestructibility indestructibility equiconsistency measurable cardinal strong cardinal hyperstrong cardinal Woodin cardinal strongly compact cardinal supercompact cardinal core model


Apter, Arthur W.; Sargsyan, Grigor. An equiconsistency for universal indestructibility. J. Symbolic Logic 75 (2010), no. 1, 314--322. doi:10.2178/jsl/1264433923.

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