Presentations of the successor relation of computable linear ordering

Abstract

We prove that a nontrivial degree spectrum of the successor relation of either strongly η-like or non-η-like computable linear orderings is closed upwards in the class of all computably enumerable degrees. We also show that the degree spectrum contains 0 if and only if either it is trivial or it contains all computably enumerable degrees. © 2010 Allerton Press, Inc.