We study Turing degrees a for which there is a countable structure  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″ \u3e 0‴

Andrews, Uri

Cai, Mingzhong

Kalimullin, Iskander Sh

Lempp, Steffen

Miller, Joseph S

Montalban, Antonio

English

Dartmouth Digital Commons (Dartmouth College)

The Complements of Lower Cones of Degrees and the Degree Spectra of Structures

Abstract. We study Turing degrees a for which there is a countable structure A whose degree spectrum is the collection {x: x 6 ≤ 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′ ′&gt; 0′′′. 1

Uri Andrews

Mingzhong Cai

Iskander Sh. Kalimullin

Steffen Lempp

Joseph S. Miller

Antonio Montalbán

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THE COMPLEMENTS OF LOWER CONES OF DEGREES AND THE DEGREE SPECTRA OF STRUCTURES

http://www.math.wisc.edu/%7Ejmiller/Papers/compcone.pdf

The Complements of Lower Cones of Degrees and the Degree Spectra of Structures

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