THE COMPLEMENTS OF LOWER CONES OF DEGREES AND THE DEGREE SPECTRA OF STRUCTURES
Uri Andrews, Mingzhong Cai, ISKANDER SH. KALIMULLIN, Steffen Lempp, Joseph S. Miller, Antonio Montalbán · Journal of Symbolic Logic · 2016
Abstract We study Turing degrees a for which there is a countable structure ${\cal A}$ whose degree spectrum is the collection {x : x ≰ a}. In particular, for degrees a from the interval [0′, 0″], such a structure exists if a′ = 0″, and there are no such structures if a″ > 0‴.