Degree Spectra of Relations on a Cone

Let \mathcal A be a mathematical structure with an additional relation R. The author is interested in the degree spectrum of R, either among computable copies of \mathcal A when (\mathcal A,R) is a "natural" structure, or (to make this rigorous) among copies of (\mathcal A,R) computable in...

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Bibliographic Details
Main Author Harrison-Trainor, Matthew
Format eBook Book
LanguageEnglish
Published Providence, Rhode Island American Mathematical Society 2018
Edition1
SeriesMemoirs of the American Mathematical Society
Subjects
Angles (Geometry)
Angles (Geometry) > Measurement
Conic sections
Unsolvability (Mathematical logic)
degree spectrum of a relation
cone of Turing degrees
computable structure
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Summary:Let \mathcal A be a mathematical structure with an additional relation R. The author is interested in the degree spectrum of R, either among computable copies of \mathcal A when (\mathcal A,R) is a "natural" structure, or (to make this rigorous) among copies of (\mathcal A,R) computable in a large degree d. He introduces the partial order of degree spectra on a cone and begin the study of these objects. Using a result of Harizanov--that, assuming an effectiveness condition on \mathcal A and R, if R is not intrinsically computable, then its degree spectrum contains all c.e. degrees--the author shows that there is a minimal non-trivial degree spectrum on a cone, consisting of the c.e. degrees.
Bibliography:Includes bibliographical references and index
May 2018, volume 253, number 1208 (third of 7 numbers)
ISBN:1470428393
9781470428396
ISSN:0065-9266
1947-6221
DOI:10.1090/memo/1208