Series: Penn State Logic Seminar Date: Tuesday, April 26, 2005 Time: 2:30 - 3:45 PM Place: 103 Pond Laboratory Speaker: John Clemens, Penn State, Mathematics Title: Separation Principles and Wadge Classes Abstract: A pointclass (i.e., a collection of subsets of some fixed Polish space) is a Wadge class if it is closed under continuous preimages. We say that a pointclass satisfies the Separation Principle if for any two disjoint sets A and B from the class, there is a set C such that both C and its complement are in the class, and C separates A from B, i.e., A is contained in C and B is disjoint from C. I will discuss variations of this principle and prove several results of Steel and Van Wesep, in particular: Assuming the Axiom of Determinacy, for any non-self-dual Wadge class on the Baire space, exactly one of the class or its dual satisfies the Separation Principle.