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Degree Spectra of Relations on a Cone
 
Matthew Harrison-Trainor University of California, Berkeley, Berkeley, California, USA
Degree Spectra of Relations on a Cone
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
eBook 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
Softcover ISBN:  978-1-4704-2839-6
eBook: ISBN:  978-1-4704-4411-2
Product Code:  MEMO/253/1208.B
List Price: $156.00 $117.00
MAA Member Price: $140.40 $105.30
AMS Member Price: $93.60 $70.20
Degree Spectra of Relations on a Cone
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Degree Spectra of Relations on a Cone
Matthew Harrison-Trainor University of California, Berkeley, Berkeley, California, USA
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
eBook 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
Softcover ISBN:  978-1-4704-2839-6
eBook ISBN:  978-1-4704-4411-2
Product Code:  MEMO/253/1208.B
List Price: $156.00 $117.00
MAA Member Price: $140.40 $105.30
AMS Member Price: $93.60 $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.

  • Table of Contents
     
     
    • 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
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    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 publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.