Classes bounded by incomplete sets Original Research Article

We study connections between strong reducibilities and properties of computably enumerable sets such as simplicity. We say that a class View the MathML source of computably enumerable sets bounded iff there is an m-incomplete computably enumerable set A such that every set in View the MathML source 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 iff B is View the MathML source. 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.