Series: Penn State Logic Seminar

 Date: Tuesday, November 29, 2005

 Time: 2:30 - 3:45 PM

 Place: 106 McAllister Building

 Speaker: Stephen G. Simpson, Penn State, Mathematics

 Title: An Introduction to Degrees of Unsolvability, part 6


   Loosely speaking, the Basis Problem reads as follows: Given a
   "tame" subset P of the Baire space which is nonempty, to find a
   "tame" member of P.  I shall present various solutions to the Basis
   Problem in the case when P is a subset of the Baire space which is
   nonempty, recursively bounded, and Pi^0_1.  In this case I shall
   show how to find members of P whose respective degrees of
   unsolvability are r.e., low, and almost recursive.  However, it is
   not in general possible to find a member of P which enjoys more
   than one of these three properties.