Series: Penn State Logic Seminar Date: Friday, May 17, 2002 Time: 2:20 - 3:35 PM Place: 304 Willard Building Speaker: Arthur Apter, Mathematics, CUNY Title: Indestructibility and Strong Compactness Abstract: In the mid 1970s, Richard Laver showed that any supercompact cardinal kappa could have its supercompactness made indestructible under kappa-directed closed forcing. I will discuss what is known concerning proving Laver's result for an arbitrary strongly compact cardinal.