Abstract:
We prove that a nontrivial degree spectrum of the successor relation of either strongly $\eta$-like or non-$\eta$-like computable linear orderings is closed upward in the class of all computably enumerable degrees. We also show that the degree spectrum contains $\mathbf0$ if and only if either it is trivial or it contains all computably enumerable degrees.
Keywords:linear orderings, successor relation, Turing degree spectra, computable presentations.
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