Series: Penn State Logic Seminar Date: Tuesday, September 17, 2002 Time: 2:30 - 3:45 PM Place: 312 Boucke Building Speaker: Stephen G. Simpson, Mathematics, Penn State Title: A Dual Form of Ramsey's Theorem Abstract: The classical Ramsey's Theorem reads as follows. Let N be a countably infinite set. If we color all k-element subsets of N with finitely many colors, then there exists an infinite subset of N all of whose k-element subsets have the same color. The Dual Ramsey Theorem, due to Carlson and Simpson, reads as follows. If we color all k-element partitions of N with finitely many Borel colors, then there exists an infinite partition of N such that all coarser k-element partitions have the same color.