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

Authors

Uri Andrews, University of Wisconsin
Mingzhong Cai, Dartmouth CollegeFollow
Iskander Sh Kalimullin, Kazan Federal University
Steffen Lempp, University of Wisconsin
Joseph S. Miller, University of Wisconsin
Antonio Montalban, University of California, Berkeley

Document Type

Article

Publication Date

2016

Publication Title

The Journal of Symbolic Logic

Department

Department of Mathematics

Abstract

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″ > 0‴.

DOI

10.1017/jsl.2015.59

Dartmouth Digital Commons Citation

Andrews, Uri; Cai, Mingzhong; Kalimullin, Iskander Sh; Lempp, Steffen; Miller, Joseph S.; and Montalban, Antonio, "The Complements of Lower Cones of Degrees and the Degree Spectra of Structures" (2016). Dartmouth Scholarship. 3395.
https://digitalcommons.dartmouth.edu/facoa/3395