The complements of lower cones of degrees and the degree spectra of structures

Abstract

© 2016, Association for Symbolic Logic.We study Turing degrees a for which there is a countable structure A whose degree spectrum is the collection {x: x ≰ a}. In particular, for degrees a from the interval [0ʹ, 0ʺ ], such a structure exists if aʹ = 0ʺ, and there are no such structures if aʺ > 0ʺʹ .