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An equiconsistency for universal indestructibility

  • Arthur W. Apter (a1) (a2) and Grigor Sargsyan (a3)


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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Department of Mathematics, University of California, Los Angeles, CA 90095, USA, E-mail:, URL:


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An equiconsistency for universal indestructibility

  • Arthur W. Apter (a1) (a2) and Grigor Sargsyan (a3)


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