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.
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Original Russian Text © A.N. Frolov, 2010, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, No. 7, pp. 73–85.
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Frolov, A.N. Presentations of the successor relation of computable linear ordering. Russ Math. 54, 64–74 (2010). https://doi.org/10.3103/S1066369X10070078
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DOI: https://doi.org/10.3103/S1066369X10070078