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.
"An equiconsistency for universal indestructibility." J. Symbolic Logic 75 (1) 314 - 322, March 2010. https://doi.org/10.2178/jsl/1264433923