Series: Penn State Logic Seminar Date: Wednesday, July 28, 2004 Time: 11:10 AM - 12:25 PM Place: 317 Boucke Building Speaker: Stephen G. Simpson, Penn State, Mathematics Title: Sharps and Projective Determinacy, part 2 Abstract: We begin with a brief history of the relationship between large cardinals and projective determinacy. After some preliminaries concerning hyperdegrees, we prove the following two results. (1) If one assumes full hyperdegree determinacy, then aleph_1 is a measurable cardinal. (2) If one assumes absolutely Delta^1_2 hyperdegree determinacy, then sharps exist.