Presentations of the successor relation of computable linear ordering
A. N. Frolov · Russian Mathematics · 2010
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.