Degrees of Unsolvability : Local and Global Theory.
This volume presents a systematic study of the interaction between local and global degree theory.
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Full Text (via Cambridge) |
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| Main Author: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge :
Cambridge University Press,
2017.
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| Series: | Perspectives in logic.
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| Subjects: |
MARC
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| 100 | 1 | |a Lerman, Manuel. | |
| 245 | 1 | 0 | |a Degrees of Unsolvability : |b Local and Global Theory. |
| 260 | |a Cambridge : |b Cambridge University Press, |c 2017. | ||
| 300 | |a 1 online resource (323 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Perspectives in logic ; |v v. 11 | |
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Cover ; Half-title ; Series information ; Title page ; Copyright information ; Dedication ; Preface to the Series ; Author's Preface ; Table of Contents ; Introduction; Part A The Structure of the Degrees; Chapter I Recursive Functions; 1. The Recursive and Partial Recursive Functions; 2. Relative Recursion; 3. The Enumeration and Recursion Theorems; Chapter II Embeddings and Extensions of Embeddings in the Degrees; 1. Upper semilattice Structure for the Degrees; 2. Incomparable Degrees; 3. Embeddings into the Degrees; 4. Extensions of Embeddings into the Degrees. | |
| 505 | 8 | |a Chapter III The Jump Operator1. The Arithmetical Hierarchy; 2. The Jump Operator; 3. Embeddings and Exact Pairs Below 0'; 4. Jump Inversion; 5. Maximal Antichains and Maximal Independent Sets Below 0'; 6. Maximal Chains Below 0'; 7. Classes of Degrees Determined by the Jump Operation; 8. More Exact Pairs; Chapter IV High/Low Hierarchies; 1. High/Low Hierarchies ; 2. GL[sub(1)] and 1-Generic Degrees; 3. GL[sub(2)] and Its Complement; 4. GH[sub(1)] ; 5. Automorphism Bases; Part B Countable Ideals of Degrees; Chapter V Minimal Degrees; 1. Binary Trees; 2. Minimal Degrees. | |
| 505 | 8 | |a 3. Double Jumps of Minimal Degrees4. Minimal Covers and Minimal Upper Bounds; 5. Cones of Minimal Covers; Chapter VI Finite Distributive Lattices; 1. Usl Representations; 2. Uniform Trees; 3. Splitting Trees; 4. Initial Segments of D ; 5. An Automorphism Base for D ; Chapter VII Finite Lattices; 1. Weakly Homogeneous Sequential Lattice Tables; 2. Uniform Trees; 3. Splitting Trees; 4. Finite Ideals of D; 5. An Automorphism Base for D ; Chapter VIII Countable Usls; 1. Countable Ideals of D ; 2. Jump Preserving Isomorphisms; 3. The Degree of Th(D) ; 4. Elementary Equivalence over D' | |
| 505 | 8 | |a 5. Isomorphisms Between Cones of DegreesPart C Initial Segments of D and the Jump Operator; Chapter IX Minimal Degrees and High/Low Hierarchies; 1. Partial Recursive Trees; 2. Minimal Degrees Below 0'; 3. Minimal Degrees Below Degrees in GH[sub(1)] ; Chapter X Jumps of Minimal Degrees; 1. Targets; 2. Jumps of Minimal Degrees; Chapter XI Bounding Minimal Degrees with Recursively Enumerable Degrees; 1. Trees Permitted by Recursively Enumerable Sets; 2. Minimal Degrees and Recursively Enumerable Permitting; Chapter XII Initial Segments of D[0,0'] ; 1. Weakly Uniform Trees. | |
| 505 | 8 | |a 2. Subtree Constructions3. Splitting Trees; 4. The Construction; 5. Generalizations and Applications; Appendix A Coding into Structures and Theories; 1. Degrees of Presentations of Lattices; 2. Interpreting Theories within Other Theories; 3. Second Order Arithmetic; Appendix B Lattice Tables and Representation Theorems; 1. Finite Distributive Lattices; 2. Finite Lattices; 3. Countable Uppersemilattices; References; Notation Index; Subject Index. | |
| 520 | |a This volume presents a systematic study of the interaction between local and global degree theory. | ||
| 650 | 0 | |a Unsolvability (Mathematical logic) | |
| 650 | 7 | |a Unsolvability (Mathematical logic) |2 fast |0 (OCoLC)fst01162046 | |
| 776 | 0 | 8 | |i Print version: |a Lerman, Manuel. |t Degrees of Unsolvability : Local and Global Theory. |d Cambridge : Cambridge University Press, ©2017 |z 9781107168138 |
| 830 | 0 | |a Perspectives in logic. | |
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