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.