Series: Penn State Logic Seminar Date: Tuesday, June 7, 2005 Time: 2:30 - 3:45 PM Place: 123 Pond Laboratory Speaker: Chi-Tat Chong, Mathematics, National University of Singapore Title: Ramsey's Theorem and Sigma_2 Induction Abstract: Ramsey's Theorem states that every k-coloring of n-element subsets of the natural numbers is monochromatic on an infinite subset. The relation between Ramsey's Theorem and first order mathematical induction, over the base theory RCA_0, is of interest from the reverse mathematics point of view. Hirst (1987) proved that over RCA_0, Ramsey's Theorem for pairs implies Sigma_2 bounding (BSigma_2). In this talk, we show that the stronger inductive scheme ISigma_2 is a consequence of this axiom system, answering a question posed by Cholak, Jockusch and Slaman.