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 Abstract: 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.