Series: Penn State Logic Seminar

 Date: Tuesday, September 13, 2005

 Time: 2:30 - 3:45 PM

 Place: 106 McAllister Building

 Speaker: Stephen G. Simpson, Penn State, Mathematics

 Title: The Reverse Mathematics of Ramsey's Theorem, part 3


  We use Mathias forcing to prove the following lemma.  Let C_i, i =
  0, 1, 2, ... be a sequence of non-recursive subsets of omega.  Let U
  be an arbitrary subset of omega.  Then there exists a subset of
  omega, A, which is either included in or disjoint from U, and such
  that for all i, C_i is not recursive relative to A.  From this
  lemma, Seetapun's Theorem will follow easily.