THE COMPLEMENTS OF LOWER CONES OF DEGREES AND THE DEGREE SPECTRA OF STRUCTURES. (15th August 2016)

• Record Type: Journal Article
• Authors: ANDREWS, URI; CAI, MINGZHONG; KALIMULLIN, ISKANDER SH.; LEMPP, STEFFEN; MILLER, JOSEPH S.; MONTALBÁN, ANTONIO
• Is Part Of: Journal of symbolic logic. Volume 81:Number 3(2016)
• Page Start: 997
• Page End: 1006
• Publication Date: 2016-08-15
• Subjects: algebraic structures, -- turing degrees, -- degree spectra, -- computably enumerable (c.e.) sets, -- families of c.e. sets; Logic, Symbolic and mathematical -- Periodicals; 511.3
• DOI: 10.1017/jsl.2015.59
• Languages: English
• ISSNs: 0022-4812

Abstract

Abstract: We study Turing degreesa for which there is a countable structure ${\cal A}$ whose degree spectrum is the collection {x :x ≰a }. In particular, for degreesa from the interval [0′, 0″], such a structure exists ifa ′ = 0″, and there are no such structures ifa ″ > 0‴.