2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77236From a suitable large cardinal hypothesis, we provide a model with a supercompact cardinal in which universal indestructibility holds: every supercompact and partially supercompact cardinal kappa is fully indestructible by kappa-directed closed forcing. Such a state of affairs is impossible with two supercompact cardinals or even with a cardinal which is supercompact beyond a measurable cardinal.Plain tex, 13 pages. Submitted to the Kobe Journal of Mathematics. See also http://www.library.csi.cuny.edu/users/hamkins/papers.html#UniversalLogic03E55; 03E40text