Abstract
AbstractLet denote the collection of all Π10 classes, ordered by inclusion. A collection of Turing degrees in is called invariant over if there is some collection of Π10 classes representing exactly the degrees such that is invariant under automorphisms of . Herein we expand the known degree invariant classes of , previously including only {0} and the array noncomputable degrees, to include all highn and non-lown degrees for n > 2. This is a corollary to a very general definability result. The result is carried out in a substructure G of , within which the techniques used model those used by Cholak and Harrington [6] to obtain the same definability for the c.e. sets. We work back and forth between G and to show that this definability in G gives the desired degree invariance over .
Publisher
Cambridge University Press (CUP)