Series: Penn State Logic Seminar Date: Tuesday, September 11, 2001 Time: 2:30 - 3:45 PM Place: 306 Boucke Building Speaker: Stephen Binns, Mathematics, Penn State Title: Medvedev Degrees of Pi01 Subsets of 2omega Abstract: Let P and Q be subsets of 2^omega, the space of infinite sequences of 0's and 1's. P is said to be Medvedev reducible to Q if there exists a Turing computable functional which carries members of Q to members of P. P and Q are said to be of the same Medvedev degree if each is Medvedev reducible to the other. The partial ordering of Medvedev degrees under Medvedev reducibility turns out to be a distributive lattice. The sublattice consisting of Medvedev degrees of Pi^0_1 subsets of 2^omega turns out to have a rich structure, which has been explored in recent research by Binns and Simpson.