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(Ebook) Degree Spectra of Relations on a Cone by Matthew Harrison-Trainor ISBN 9781470444112, 1470444119

  • SKU: EBN-51631734
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Authors:Matthew Harrison-Trainor
Pages:120 pages.
Year:2018
Editon:1
Publisher:American Mathematical Society
Language:english
File Size:1.12 MB
Format:pdf
ISBNS:9781470444112, 1470444119
Categories: Ebooks

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(Ebook) Degree Spectra of Relations on a Cone by Matthew Harrison-Trainor ISBN 9781470444112, 1470444119

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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