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Degree Spectra of Relations on a Cone 1st Edition by Matthew Harrison Trainor ISBN 9781470444112 1470444119

Name: Degree Spectra of Relations on a Cone 1st Edition by Matthew Harrison Trainor ISBN 9781470444112 1470444119
SKU: EB-51631734
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Degree Spectra of Relations on a Cone 1st Edition Matthew Harrison-Trainor Digital Instant Download

Author(s): Matthew Harrison-Trainor

ISBN(s): 9781470444112, 1470444119

Edition: 1

File Details: PDF, 1.12 MB

Year: 2018

Language: English

SKU: EB-51631734 Category: Uncategorized Tag: Matthew Harrison-Trainor

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Degree Spectra of Relations on a Cone 1st Edition by Matthew Harrison Trainor – Ebook PDF Instant Download/Delivery: 9781470444112 ,1470444119
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ISBN 10: 1470444119
ISBN 13: 9781470444112
Author: Matthew Harrison Trainor

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.

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