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
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| Vydanie: | 1 |
| Edícia: | Memoirs of the American Mathematical Society |
| Predmet: | |
| ISBN: | 1470428393, 9781470428396 |
| ISSN: | 0065-9266, 1947-6221 |
| On-line prístup: | Získať plný text |
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Obsah:
- 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