Universal Indestructibility
arXiv:math/9808004
Abstract
From 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#Universal