Series: Penn State Logic Seminar

 Date: Tuesday, November 1, 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 3


   We explore the relationships among the arithmetical hierarchy over
   omega, the Turing jump operator, and degrees of unsolvability.  We
   use these concepts to clarify some basic mathematical distinctions:
   decidability versus undecidability, provability versus truth,
   completeness versus incompleteness, explicit versus implicit
   definability.  After that, we return to the idea of oracle programs
   in order to introduce the arithmetical hierarchy over the Baire
   space.  We then begin our discussion of basis theorems and mass