Sharps and Projective Determinacy, part 1

Series: Penn State Logic Seminar

Date: Wednesday, July 21, 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 1
        
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.