Series: Penn State Logic Seminar

Date: Tuesday, June 28, 2005

Time: 2:30 - 3:45 PM

Place: 123 Pond Laboratory

Speaker: Carl Mummert, Mathematics, Penn State

Title: Reverse Mathematics and Hindman's Theorem, part 1

Abstract:

  Hindman's theorem states that if the natural numbers are colored
  with finitely many colors then there is an infinite set D of natural
  numbers such that all sums of finite subsets of D receive the same
  color. Blass, Hirst, and Simpson (1987) showed that Hindman's
  theorem is provable in ACA_0^+ and implies ACA_0 over RCA_0. The
  exact strength of Hindman's theorem is not known.  Hirst (2004) has
  shown that certain special cases of Hindman's theorem are provable
  in ACA_0. This talk will cover Hirst's recent results in detail.