Series: Penn State Logic Seminar Date: Tuesday, March 4, 2003 Time: 2:30 - 3:45 PM Place: 113 McAllister Building Speaker: Stephen G. Simpson, Penn State, Mathematics Title: Some Results Concerning Muchnik Degrees, part 1 Abstract: Let P and Q be sets of reals. P is said to be Muchnik reducible to Q if every member of Q Turing-computes a member of P. A Muchnik degree is an equivalence class of sets of reals under mutual Muchnik reducibility. It is easy to see that the Muchnik degrees form a distributive lattice under the partial ordering induced by Muchnik reducibility. Call this lattice L. We study not only L but also its distributive sublattice L_0 consisting of the Muchnik degrees of nonempty Pi^0_1 subsets of the closed unit interval [0,1]. We present a variety of results and techniques which have been useful in recent investigations.
Lecture notes are available here.