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,...
Gespeichert in:
| Körperschaft: | |
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| Weitere Verfasser: | , |
| Format: | Elektronisch Tagungsbericht E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
1980.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
45. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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, as a branch of mathematical logic. This book is a collection of advanced research/survey papers by eminent research workers in the field, based on their lectures given at the Leeds Logic Colloquium 1979. As such it provides an up-to-date view of current ideas and developments in the field of recursion theory as a whole. The individual contributions fit together naturally so as to provide an overview of all the main areas of research in the field. It will therefore be an important and invaluable source for advanced researchers and research students in mathematics and computer science (particularly in Europe, USA and USSR). |
| Beschreibung: | 1 online resource (319 pages) |
| Bibliographie: | Includes bibliographical references. |
| ISBN: | 9781107360969 110736096X 9780511629181 0511629184 1139881558 9781139881555 1107365872 9781107365872 1107370604 9781107370609 1107368332 9781107368330 1299403689 9781299403680 1107363411 9781107363410 |
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| 520 | |a 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, as a branch of mathematical logic. This book is a collection of advanced research/survey papers by eminent research workers in the field, based on their lectures given at the Leeds Logic Colloquium 1979. As such it provides an up-to-date view of current ideas and developments in the field of recursion theory as a whole. The individual contributions fit together naturally so as to provide an overview of all the main areas of research in the field. It will therefore be an important and invaluable source for advanced researchers and research students in mathematics and computer science (particularly in Europe, USA and USSR). | ||
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a ""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 | |
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| author2 | Drake, F. R. (Frank Robert) Wainer, S. S. |
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| author_corporate | Logic Colloquium Leeds, England |
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| contents | 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 |
| ctrlnum | (OCoLC)839304926 |
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| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
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| discipline | Mathematik |
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| genre | Conference papers and proceedings fast |
| genre_facet | Conference papers and proceedings |
| id | ZDB-4-EBA-ocn839304926 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:25:17Z |
| institution | BVB |
| isbn | 9781107360969 110736096X 9780511629181 0511629184 1139881558 9781139881555 1107365872 9781107365872 1107370604 9781107370609 1107368332 9781107368330 1299403689 9781299403680 1107363411 9781107363410 |
| language | English |
| oclc_num | 839304926 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (319 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 1980 |
| publishDateSearch | 1980 |
| publishDateSort | 1980 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | London Mathematical Society lecture note series ; |
| series2 | London Mathematical Society lecture note series ; |
| spelling | Logic Colloquium (1979 : Leeds, England) Recursion theory : its generalisations and applications : proceedings of Logic Colloquium '79, Leeds, August 1979 / edited by F.R. Drake and S.S. Wainer. Cambridge ; New York : Cambridge University Press, 1980. 1 online resource (319 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 45 Includes bibliographical references. Print version record. 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, as a branch of mathematical logic. This book is a collection of advanced research/survey papers by eminent research workers in the field, based on their lectures given at the Leeds Logic Colloquium 1979. As such it provides an up-to-date view of current ideas and developments in the field of recursion theory as a whole. The individual contributions fit together naturally so as to provide an overview of all the main areas of research in the field. It will therefore be an important and invaluable source for advanced researchers and research students in mathematics and computer science (particularly in Europe, USA and USSR). 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 English. Recursion theory Congresses. Théorie de la récursivité Congrès. MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Recursion theory fast Conference papers and proceedings fast Drake, F. R. (Frank Robert) https://id.oclc.org/worldcat/entity/E39PCjCkwpPt8grFg3cvp4GYCP http://id.loc.gov/authorities/names/n82132141 Wainer, S. S. Print version: Logic Colloquium (1979 : Leeds, England). Recursion theory. Cambridge ; New York : Cambridge University Press, 1980 052123543X (DLC) 82180570 (OCoLC)502528916 London Mathematical Society lecture note series ; 45. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552383 Volltext |
| spellingShingle | Recursion theory : its generalisations and applications : proceedings of Logic Colloquium '79, Leeds, August 1979 / London Mathematical Society lecture note series ; 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 Recursion theory Congresses. Théorie de la récursivité Congrès. MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Recursion theory fast |
| title | Recursion theory : its generalisations and applications : proceedings of Logic Colloquium '79, Leeds, August 1979 / |
| title_auth | Recursion theory : its generalisations and applications : proceedings of Logic Colloquium '79, Leeds, August 1979 / |
| title_exact_search | Recursion theory : its generalisations and applications : proceedings of Logic Colloquium '79, Leeds, August 1979 / |
| title_full | Recursion theory : its generalisations and applications : proceedings of Logic Colloquium '79, Leeds, August 1979 / edited by F.R. Drake and S.S. Wainer. |
| title_fullStr | Recursion theory : its generalisations and applications : proceedings of Logic Colloquium '79, Leeds, August 1979 / edited by F.R. Drake and S.S. Wainer. |
| title_full_unstemmed | Recursion theory : its generalisations and applications : proceedings of Logic Colloquium '79, Leeds, August 1979 / edited by F.R. Drake and S.S. Wainer. |
| title_short | Recursion theory : |
| title_sort | recursion theory its generalisations and applications proceedings of logic colloquium 79 leeds august 1979 |
| title_sub | its generalisations and applications : proceedings of Logic Colloquium '79, Leeds, August 1979 / |
| topic | Recursion theory Congresses. Théorie de la récursivité Congrès. MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Recursion theory fast |
| topic_facet | Recursion theory Congresses. Théorie de la récursivité Congrès. MATHEMATICS Infinity. MATHEMATICS Logic. Recursion theory Conference papers and proceedings |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552383 |
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