An equiconsistency for universal indestructibility. (English) Zbl 1184.03051

Summary: 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.


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