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

Abstract

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.