| Description |
1 online resource (323 pages) |
| Series |
Perspectives in logic ; v. 11 |
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Perspectives in logic.
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| Contents |
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 |
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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 |
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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' |
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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 |
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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 |
| Summary |
This volume presents a systematic study of the interaction between local and global degree theory |
| Notes |
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the eleventh publication in the Perspectives in Logic series, Manuel Lerman presents a systematic study of the interaction between local and global degree theory. He introduces the reader to the fascinating combinatorial methods of recursion theory while simultaneously showing how to use these methods to prove global theorems about degrees. The intended reader will have already taken a graduate-level course in recursion theory, but this book will also be accessible to those with some background in mathematical logic and a feeling for computability. It will prove a key reference to enable readers to easily locate facts about degrees and it will direct them to further results |
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Print version record |
| Subject |
Unsolvability (Mathematical logic)
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Soluciones numéricas
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Unsolvability (Mathematical logic)
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| Form |
Electronic book
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| ISBN |
9781316749005 |
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1316749002 |
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1316752860 |
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9781316752869 |
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9781316717059 |
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1316717054 |
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