Series: Penn State Logic Seminar Date: Tuesday, November 6, 2001 Time: 2:30 - 3:45 PM Place: 306 Boucke Building Speaker: Tamara Lakins, Allegheny College, Mathematics Title: Ramsey's Theorem and Computability Theory Abstract: An infinite version of Ramsey's theorem states that for every coloring of [omega]^n (the set of all n-element subsets of omega) by finitely many colors, there is an infinite set A which is homogeneous for that coloring, i.e., all elements of [A]^n have the same color. We present a survey of results and open questions concerning the complexity of infinite homogeneous sets for effectively given (computable or computably enumerable) colorings.