Series: Penn State Logic Seminar Date: Tuesday, October 25, 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 2 Abstract: In the previous talk we discussed computable functions, the Halting Problem, many-one reducibility, recursive enumerability, and the arithmetical hierarchy. In this talk we shall discuss Turing oracles, Turing reducibility, and the Turing jump operator. These fundamental concepts provide a method of comparing and classifying unsolvable problems, according to their degrees of unsolvability. We shall discuss a theorem due to Post which exposes a close relationship between degrees of unsovability and the arithmetical hierarchy.