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


  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