Kolmogorov Complexity, Strong Reducibilities, and Computably Enumerable Sets

114 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2000.We also study connections between strong reducibilities and properties of computably enumerable sets such as simplicity. We call a class S of computably enumerable sets bounded if there is an m-incomplete computably enumerable set A such that every set in S is m-reducible to A. For example, we show that the class of effectively simple sets is bounded; but the class of maximal sets is not. Furthermore, the class of computably enumerable sets Turing reducible to a computably enumerable set B is bounded if and only if B is low2. For r = bwtt, tt, wtt, and T, there is a bounded class intersecting every computably enumerable r-degree; for r = c, d and p, no such class exists.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD