Journal of Mathematical Logic 10 (1):83-99 (2010)

Abstract
In this paper, we solve a long-standing open question, about the spectrum of the successivity relation on a computable linear ordering. We show that if a computable linear ordering [Formula: see text] has infinitely many successivities, then the spectrum of the successivity relation is closed upwards in the computably enumerable Turing degrees. To do this, we use a new method of constructing [Formula: see text]-isomorphisms, which has already found other applications such as Downey, Kastermans and Lempp [9] and is of independent interest. It would seem to promise many further applications.
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DOI 10.1142/S0219061310000924
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Degrees Coded in Jumps of Orderings.Julia F. Knight - 1986 - Journal of Symbolic Logic 51 (4):1034-1042.

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