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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| Hlavný autor: | |
|---|---|
| Médium: | E-kniha Kniha |
| Jazyk: | English |
| Vydavateľské údaje: |
Providence, Rhode Island
American Mathematical Society
2018
|
| Vydanie: | 1 |
| Edícia: | Memoirs of the American Mathematical Society |
| Predmet: | |
| ISBN: | 1470428393, 9781470428396 |
| ISSN: | 0065-9266, 1947-6221 |
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| Abstract | 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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| AbstractList | 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. Let |
| Author | Harrison-Trainor, Matthew |
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| Copyright | Copyright 2018 American Mathematical Society |
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| DOI | 10.1090/memo/1208 |
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| Edition | 1 |
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| Keywords | degree spectrum of a relation cone of Turing degrees computable structure |
| LCCN | 2018017354 |
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| Language | English |
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| Notes | Includes bibliographical references and index May 2018, volume 253, number 1208 (third of 7 numbers) |
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| Snippet | Let 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... 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... |
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| SubjectTerms | Angles (Geometry) Angles (Geometry) -- Measurement Conic sections Unsolvability (Mathematical logic) |
| TableOfContents | Introduction
--
Preliminaries
--
Degree Spectra between the C.E. Degrees and the D.C.E. Degrees
--
Degree Spectra of Relations on the Naturals
--
A “Fullness” Theorem for 2-CEA\xspace Degrees
--
Further Questions
--
Relativizing Harizanov’s Theorem on C.E. Degrees Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Preliminaries -- 2.1. Computability Theory -- 2.2. Computable Structure Theory -- 2.3. Relativizing to a Cone -- Chapter 3. Degree Spectra between the C.E. Degrees and the D.C.E. Degrees -- 3.1. Necessary and Sufficient Conditions to be Intrinsically of C.E. Degree -- 3.2. Incomparable Degree Spectra of D.C.E. Degrees -- Chapter 4. Degree Spectra of Relations on the Naturals -- Chapter 5. A "Fullness" Theorem for 2-\cea Degrees -- 5.1. Approximating a 2-\cea Set -- 5.2. Basic Framework of the Construction -- 5.3. An Informal Description of the Construction -- 5.4. The Game Gs and the Final Condition -- 5.5. Basic Plays and the Basic Game -- 5.6. The Construction -- Chapter 6. Further Questions -- Appendix A. Relativizing Harizanov's Theorem on C.E. Degrees -- A.1. Framework of the Proof -- A.2. The First Two Cases -- A.3. The Third Case -- Bibliography -- Index of Notation and Terminology -- Back Cover |
| Title | Degree Spectra of Relations on a Cone |
| URI | https://www.ams.org/memo/1208/ https://cir.nii.ac.jp/crid/1130282272750515456 https://ebookcentral.proquest.com/lib/[SITE_ID]/detail.action?docID=5409180 https://www.vlebooks.com/vleweb/product/openreader?id=none&isbn=9781470444112 |
| Volume | 253 |
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