Series: Penn State Logic Seminar Date: Tuesday, July 5, 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 2 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.