Mass problems and almost everywhere domination

We examine the concept of almost everywhere domination from the viewpoint of mass problems. Let AED and MLR be the set of reals which are almost everywhere dominating and Martin-L¨of random, respectively. Let b1, b2, b3 be the degrees of unsolvability of the mass problems associated with the sets AED, MLR×AED, MLR∩AED respectively. Let Pw be the lattice of degrees of unsolvability of mass problems associated with nonempty Π0 1 subsets of 2ω . Let 1 and 0 be the top and bottom elements of Pw. We show that inf(b1, 1) and inf(b2, 1) and inf(b3, 1) belong to Pw

• Type: Journal
• Year: 2007
• Where: MLQ
• Authors: Stephen G. Simpson
• Keywords: Martin-L¨of Random, Mass Problems, MLQ 2007, Viewpoint