Laver indestructibility and the class of compact cardinals

Using an idea developed in joint work with Shelah, we show how to redefine Laver's notion of forcing making a supercompact cardinal kappa indestructible under kappa-directed closed forcing to give a new proof of the Kimchi-Magidor Theorem in which every compact cardinal in the universe (supercompact or strongly compact) satisfies certain indestructibility properties. Specifically, we show that if K is the class of supercompact cardinals in the ground model, then it is possible to force and construct a generic extension in which the only strongly compact cardinals are the elements of K or their measurable limit points, every kappa is an element of K is a supercompact cardinal indestructible under kappa-directed closed forcing, and every kappa a measurable limit point of K is a strongly compact cardinal indestructible under kappa-directed closed forcing not changing rho(kappa). We then derive as a corollary a model for the existence of a strongly compact cardinal kappa which is not kappa(+) supercompact but which is indestructible under kappa-directed closed forcing not changing rho(kappa) and remains non-kappa(+) supercompact after such a forcing has been done.