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 Abstract: 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 problems.