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Recursion theory : its generalisations and applications : proceedings of Logic Colloquium '79, Leeds, August 1979 /
Recursion theory - now a well-established branch of pure mathematics, having grown rapidly over the last 35 years - deals with the general (abstract) theory of those operations which we conceive as being `computable' by idealized machines. The theory grew out of, and is usually still regarded,...
| Clasificación: | Libro Electrónico |
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| Autor Corporativo: | |
| Otros Autores: | , |
| Formato: | Electrónico Congresos, conferencias eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
1980.
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| Colección: | London Mathematical Society lecture note series ;
45. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Degrees of Generic Sets1. INTRODUCTION; 2. PRELIMINARIES ON FORCING, GENERICITY, AND CATEGORY; 3. CONSEQUENCES OF CLASSICAL CONSTRUCTIONS; 4. MARTIN'S CATEGORY THEOREM; 5. RELATIVE RECURSIVE ENUMERABILITY OF I-GENERIC DEGREES; 6. CUPPING AND COMPLEMENTATION THEOREMS; 7. OPEN QUESTIONS; REFERENCES; The Degrees of Unsolvability: Some Recent Results; INTRODUCTION; 1. LOCAL STRUCTURE THEOREMS; 2. DECIDABILITY; 3. HOMOGENEITY; 4. AUTOMDRPHISMS; 5. DEFINABILITY; REFERENCES; GENERALISATIONS; Some Constructions in a-Recursion Theory; 1 PRELIMINARIES
- 2 a-FINITE INJURY PRIORITY ARGUMENTS AND THE SACKS SPLITTINGTHEOREM3. A CONE OF WELL ORDERED a-DEGREES; 4. MINIMAL PAIRS OF a-R.E. DEGREES; REFERENCES; The Recursion Theory of the Continuous Functionals; INTRODUCTION; BASIC DEFINITIONS AND RESULTS; THE MODULUS OF A SEQUENCE; COROLLARY (Normann-Wainer [18]); THE PROJECTIVE HIERARCHY; FINAL REMARKS; REFERENCES; Three Aspects of Recursive Enumerability in Higher Types; ABSTRACT; 1. INTRODUCTION; 2. MACHINERY; 3. INADMISSIBLE FORCING; 4. LIMITS OF RECURSIVE ENUMERABILITY; 5. COUNTABLE E-CLOSED ORDINALS; 6. POST'S PROBLEM
- 7. LOGIC ON E-CLOSED SETSREFERENCES; APPLICATIONS; Computing in Algebraic Systems; INTRODUCTION; 1. FINITE ALGORITHMIC PROCEDURES; 2. THE FAP-COMPUTABLE FUNCTIONS IN THE LARGE; 3. ALGEBRAIC INFLUENCES ON FAP-COMPUTATION; 4. LOCAL FAPCS-ENUMERATION, SEARCH AND PAIRING; 5. COUNTING AND STACKING: VARIETIES AND LOCAL FINITENESS; 6. TOPOLOGICAL ALGEBRAS; REFERENCES; Applications of Classical Recursion Theory to Computer Science; Introduction; Programming Tools; Complexity; Inductive Inference; Summary; Acknowledgements; References
- ""Natural"" Programming Languages and Complexity Measures for Subrecursive Programming Languages: An Abstract Approach1 INTRODUCTION; 2 SUBRECURSIVE PROGRAMMING LANGUAGES; 3 COMPLEXITY MEASURES; 4 SUBRECURSIVE COMPLEXITY: A BEGINNING; 5 RELATIONSHIPS BETWEEN THE COMPLEXITIES OF RELATED PROGRAMS; 6 A PROOF TECHNIQUE FOR SUBRECURSIVE COMPLEXITY; 7 OTHER SUBRECURSIVE COLLECTIONS OF FUNCTIONS J; 8 CONCLUSIONS AND QUESTIONS; 9 ACKNOWLEDGMENTS; REFERENCES; Complexity Theory with Emphasis on the Complexity of Logical Theories; LECTURE 1. BASIC COMPLEXITY THEORY