February 12
Indestructibility results of large cardinals have been an area of interest since Laver's 1978 proof that the supercompactness of $\kappa$ may be made indestructible by any $<\kappa$-directed closed forcing. I will present a continuation of this work, showing that $\alpha$-subcompact cardinals may be made suitably indestructible, but that for C(n)-supercompact cardinals this is largely not possible.