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

Published online by Cambridge University Press:  15 August 2016

URI ANDREWS ,
MINGZHONG CAI ,
ISKANDER SH. KALIMULLIN ,
STEFFEN LEMPP ,
JOSEPH S. MILLER  and
ANTONIO MONTALBÁN
URI ANDREWS
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF WISCONSIN 480 LINCOLN DR. MADISON, WI 53706, USA E-mail: andrews@math.wisc.edu URL: www.math.wisc.edu/∼andrews
MINGZHONG CAI
Affiliation:
DEPARTMENT OF MATHEMATICS DARTMOUTH COLLEGE HANOVER, NH 03755, USA E-mail: mingzhong.cai@dartmouth.edu URL: math.dartmouth.edu/∼cai
ISKANDER SH. KALIMULLIN
Affiliation:
INSTITUTE OF MATHEMATICS AND MECHANICS KAZAN FEDERAL UNIVERSITY KREMLEVSKAYA ST. 18 420008 KAZAN, RUSSIA E-mail: Iskander.Kalimullin@kpfu.ru URL: kpfu.ru/main?p_id=10721
STEFFEN LEMPP
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF WISCONSIN 480 LINCOLN DR. MADISON, WI 53706, USA E-mail: lempp@math.wisc.edu URL: www.math.wisc.edu/∼lempp
JOSEPH S. MILLER
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF WISCONSIN 480 LINCOLN DR. MADISON, WI 53706, USA E-mail: jmiller@math.wisc.edu URL: www.math.wisc.edu/∼jmiller
ANTONIO MONTALBÁN
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF CALIFORNIA-BERKELEY EVANS HALL #3840 BERKELEY, CA 94720, USA E-mail: antonio@math.berkeley.edu URL: www.math.berkeley.edu/∼antonio
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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‴.

Keywords

algebraic structuresturing degreesdegree spectracomputably enumerable (c.e.) setsfamilies of c.e. sets

Information

Type
Articles
Information
The Journal of Symbolic Logic , Volume 81 , Issue 3 , September 2016 , pp. 997 - 1006
Copyright
Copyright © The Association for Symbolic Logic 2016 

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References

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