Degree spectra of the successor relation of computable linear orderings

We establish that for every computably enumerable (c.e.) Turing degree b the upper cone of c.e. Turing degrees determined by b is the degree spectrum of the successor relation of some computable linear ordering. This follows from our main result, that for a large class of linear orderings the degree spectrum of the successor relation is closed upward in the c.e. Turing degrees. © 2008 Springer-Verlag

A note on Δ 2 0 -Spectra of linear orderings and degree spectra of the successor relation

In this paper we construct linear orderings whoseΔ 2 0 -spectra coincide with classes of all high0 and high1 degrees, respectively. We also prove that there exists a computable linear ordering such that its degree spectrum of the successor relation coincides with a fixed nonempty class of degrees which represents a Σ 1 0 -spectrum of some Ø′-computable linear ordering. © 2013 Allerton Press, Inc