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Degree Spectra of Relations on a Cone

Matthew Harrison-Trainor University of California, Berkeley, Berkeley, California, USA
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Softcover ISBN: 978-1-4704-2839-6
Product Code: MEMO/253/1208
List Price: $78.00 MAA Member Price:$70.20
AMS Member Price: $46.80 Electronic ISBN: 978-1-4704-4411-2 Product Code: MEMO/253/1208.E List Price:$78.00
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AMS Member Price: $70.20 Click above image for expanded view Degree Spectra of Relations on a Cone Matthew Harrison-Trainor University of California, Berkeley, Berkeley, California, USA Available Formats:  Softcover ISBN: 978-1-4704-2839-6 Product Code: MEMO/253/1208  List Price:$78.00 MAA Member Price: $70.20 AMS Member Price:$46.80
 Electronic ISBN: 978-1-4704-4411-2 Product Code: MEMO/253/1208.E
 List Price: $78.00 MAA Member Price:$70.20 AMS Member Price: $46.80 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$117.00 MAA Member Price: $105.30 AMS Member Price:$70.20
• Book Details

Memoirs of the American Mathematical Society
Volume: 2532018; 107 pp
MSC: Primary 03;

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.

• Chapters
• 1. Introduction
• 2. Preliminaries
• 3. Degree Spectra between the C.E. Degrees and the D.C.E. Degrees
• 4. Degree Spectra of Relations on the Naturals
• 5. A “Fullness” Theorem for 2-CEA\xspace Degrees
• 6. Further Questions
• A. Relativizing Harizanov’s Theorem on C.E. Degrees

• Requests

Review Copy – for reviewers who would like to review an AMS book
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Accessibility – to request an alternate format of an AMS title
Volume: 2532018; 107 pp
MSC: Primary 03;

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.

• Chapters
• 1. Introduction
• 2. Preliminaries
• 3. Degree Spectra between the C.E. Degrees and the D.C.E. Degrees
• 4. Degree Spectra of Relations on the Naturals
• 5. A “Fullness” Theorem for 2-CEA\xspace Degrees
• 6. Further Questions
• A. Relativizing Harizanov’s Theorem on C.E. Degrees
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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