Verfügbarkeit: Fundamentals of mathematical logic

Fundamentals of mathematical logic:

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1. Verfasser:	Hinman, Peter G. (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Wellesley, Mass. A. K. Peters 2005
Schlagworte:	Lógica matemática (textos avançados) Wiskundige logica Logic, Symbolic and mathematical Model theory Set theory Recursion theory Mathematische Logik
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	XVI, 878 S. graph. Darst.
ISBN:	1568812620

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MARC


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Datensatz im Suchindex

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adam_text	FUNDAMENTALS OF MATHEMATICAL LOGIC PETER G. HINMAN UNIVERSITY OF MICHIGAN A K PETERS WELLESLEY, MASSACHUSETTS CONTENTS PREFACE XI INTRODUCTION 1 1. PROPOSITIONAL LOGIC AND OTHER FUNDAMENTALS . . . . 13 1.1. THE PROPOSITIONAL LANGUAGE 13 1.2. INDUCTION AND RECURSION 20 INDUCTION 20 RECURSION 25 1.3. PROPOSITIONAL SEMANTICS 32 1.4. PROPOSITIONAL THEORIES 41 GENERAL PROPERTIES 42 COMPACTNESS 47 1.5. DECIDABILITY AND EFFECTIVE ENUMERABILITY 54 1.6. OTHER CONSTRUCTIONS 63 NOTIONS OF CONSISTENCY 63 ULTRAPRODUCTS 67 1.7. TOPOLOGY AND BOOLEAN ALGEBRA .72 TOPOLOGY 73 BOOLEAN ALGEBRA 74 VIII CONTENTS 2. FIRST-ORDER LOGIC 83 2.1. SYNTAX AND SEMANTICS OF FIRST-ORDER LANGUAGES 83 2.2. BASIC SEMANTICS 96 SUBSTITUTION 105 2.3. STRUCTURES 114 ISOMORPHISM AND EQUIVALENCE 115 SUBSTRUCTURES 119 PRODUCTS AND CHAINS 130 2.4. THEORIES 139 THE LANGUAGE OF EQUALITY 149 DENSE LINEAR ORDERINGS 154 2.5. ARITHMETIC 160 2.6. CHANGING LANGUAGES 173 INTERPRETATIONS 186 3. COMPLETENESS AND COMPACTNESS 193 3.1. COUNTABLE COMPACTNESS 194 3.2. COUNTABLE COMPLETENESS 204 3.3. OTHER CONSTRUCTIONS 216 NOTIONS OF CONSISTENCY 216 ULTRAPRODUCTS 224 BOOLEAN ALGEBRA 228 3.4. UNCOUNTABLE LANGUAGES AND STRUCTURES 236 3.5. APPLICATIONS OF COMPACTNESS 249 3.6. HIGHER-ORDER LOGIC 276 MONADIC SECOND-ORDER LOGIC 276 3.7. INFINITARY LOGIC 293 4. INCOMPLETENESS AND UNDECIDABILITY 309 4.1. A FIRST LOOK 310 4.2. RECURSIVE FUNCTIONS AND RELATIONS 326 4.3. RECURSIVELY ENUMERABLE SETS AND RELATIONS 341 4.4. GODEL NUMBERING . . 352 4.5. DEFINABILITY IN ARITHMETIC I 364 4.6. REPRESENTABILITY: FIRST INCOMPLETENESS THEOREM 369 5. TOPICS IN DEFINABILITY 393 5.1. DEFINABILITY IN ARITHMETIC II 393 5.2. INDEXING 409 5.3. SECOND INCOMPLETENESS THEOREM 421 CONTENTS IX 5.4. CHURCH S THESIS 431 RECURSION EQUATIONS 432 ABSTRACT MACHINES 436 5.5. APPLICATIONS TO OTHER LANGUAGES AND THEORIES 443 6. SET THEORY 455 6.1. ZERMELO-FRAENKEL SET THEORY 456 6.2. MATHEMATICS IN SET THEORY I 472 6.3. ORDINAL NUMBERS: INDUCTION AND RECURSION 497 6.4. CARDINAL NUMBERS 510 6.5. MODELS AND INDEPENDENCE 527 6.6. MATHEMATICS IN SET THEORY II 550 6.7. THE CONSTRUCTIBLE UNIVERSE 567 6.8. GENERIC EXTENSIONS 577 6.9. FORCING 596 6.10. LARGE CARDINALS 605 6.11. DETERMINACY 622 7. MODEL THEORY 655 7.1. PARTIAL EMBEDDINGS 655 7.2. BOOLEAN ALGEBRAS, ULTRAFILTERS AND TYPES 671 7.3. COUNTABLE MODELS OF COUNTABLE THEORIES 683 7.4. UNCOUNTABLE MODELS OF COUNTABLE THEORIES 700 7.5. MORLEY S THEOREM 708 7.6. ABSTRACT LOGICS 721 8. RECURSION THEORY 733 8.1. MANY-ONE DEGREES AND R.E. SETS 733 8.2. TURING REDUCIBILITY 756 8.3. THE JUMP OPERATOR 770 8.4. UPPER BOUNDS 783 8.5. JUMPS OF R.E. SETS 793 8.6. LOWER BOUNDS 808 REFERENCES 821 ITEM REFERENCES 829 SYMBOL INDEX 835 SUBJECT INDEX 855
adam_txt	FUNDAMENTALS OF MATHEMATICAL LOGIC PETER G. HINMAN UNIVERSITY OF MICHIGAN A K PETERS WELLESLEY, MASSACHUSETTS CONTENTS PREFACE XI INTRODUCTION 1 1. PROPOSITIONAL LOGIC AND OTHER FUNDAMENTALS . . . . 13 1.1. THE PROPOSITIONAL LANGUAGE 13 1.2. INDUCTION AND RECURSION 20 INDUCTION 20 RECURSION 25 1.3. PROPOSITIONAL SEMANTICS 32 1.4. PROPOSITIONAL THEORIES 41 GENERAL PROPERTIES 42 COMPACTNESS 47 1.5. DECIDABILITY AND EFFECTIVE ENUMERABILITY 54 1.6. OTHER CONSTRUCTIONS 63 NOTIONS OF CONSISTENCY 63 ULTRAPRODUCTS 67 1.7. TOPOLOGY AND BOOLEAN ALGEBRA .72 TOPOLOGY 73 BOOLEAN ALGEBRA 74 VIII CONTENTS 2. FIRST-ORDER LOGIC 83 2.1. SYNTAX AND SEMANTICS OF FIRST-ORDER LANGUAGES 83 2.2. BASIC SEMANTICS 96 SUBSTITUTION 105 2.3. STRUCTURES 114 ISOMORPHISM AND EQUIVALENCE 115 SUBSTRUCTURES 119 PRODUCTS AND CHAINS 130 2.4. THEORIES 139 THE LANGUAGE OF EQUALITY 149 DENSE LINEAR ORDERINGS 154 2.5. ARITHMETIC 160 2.6. CHANGING LANGUAGES 173 INTERPRETATIONS 186 3. COMPLETENESS AND COMPACTNESS 193 3.1. COUNTABLE COMPACTNESS 194 3.2. COUNTABLE COMPLETENESS 204 3.3. OTHER CONSTRUCTIONS 216 NOTIONS OF CONSISTENCY 216 ULTRAPRODUCTS 224 BOOLEAN ALGEBRA 228 3.4. UNCOUNTABLE LANGUAGES AND STRUCTURES 236 3.5. APPLICATIONS OF COMPACTNESS 249 3.6. HIGHER-ORDER LOGIC 276 MONADIC SECOND-ORDER LOGIC 276 3.7. INFINITARY LOGIC 293 4. INCOMPLETENESS AND UNDECIDABILITY 309 4.1. A FIRST LOOK 310 4.2. RECURSIVE FUNCTIONS AND RELATIONS 326 4.3. RECURSIVELY ENUMERABLE SETS AND RELATIONS 341 4.4. GODEL NUMBERING . . 352 4.5. DEFINABILITY IN ARITHMETIC I 364 4.6. REPRESENTABILITY: FIRST INCOMPLETENESS THEOREM 369 5. TOPICS IN DEFINABILITY 393 5.1. DEFINABILITY IN ARITHMETIC II 393 5.2. INDEXING 409 5.3. SECOND INCOMPLETENESS THEOREM 421 CONTENTS IX 5.4. CHURCH'S THESIS 431 RECURSION EQUATIONS 432 ABSTRACT MACHINES 436 5.5. APPLICATIONS TO OTHER LANGUAGES AND THEORIES 443 6. SET THEORY 455 6.1. ZERMELO-FRAENKEL SET THEORY 456 6.2. MATHEMATICS IN SET THEORY I 472 6.3. ORDINAL NUMBERS: INDUCTION AND RECURSION 497 6.4. CARDINAL NUMBERS 510 6.5. MODELS AND INDEPENDENCE 527 6.6. MATHEMATICS IN SET THEORY II 550 6.7. THE CONSTRUCTIBLE UNIVERSE 567 6.8. GENERIC EXTENSIONS 577 6.9. FORCING 596 6.10. LARGE CARDINALS 605 6.11. DETERMINACY 622 7. MODEL THEORY 655 7.1. PARTIAL EMBEDDINGS 655 7.2. BOOLEAN ALGEBRAS, ULTRAFILTERS AND TYPES 671 7.3. COUNTABLE MODELS OF COUNTABLE THEORIES 683 7.4. UNCOUNTABLE MODELS OF COUNTABLE THEORIES 700 7.5. MORLEY'S THEOREM 708 7.6. ABSTRACT LOGICS 721 8. RECURSION THEORY 733 8.1. MANY-ONE DEGREES AND R.E. SETS 733 8.2. TURING REDUCIBILITY 756 8.3. THE JUMP OPERATOR 770 8.4. UPPER BOUNDS 783 8.5. JUMPS OF R.E. SETS 793 8.6. LOWER BOUNDS 808 REFERENCES 821 ITEM REFERENCES 829 SYMBOL INDEX 835 SUBJECT INDEX 855
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spellingShingle	Hinman, Peter G. Fundamentals of mathematical logic Lógica matemática (textos avançados) larpcal Wiskundige logica gtt Logic, Symbolic and mathematical Model theory Set theory Recursion theory Mathematische Logik (DE-588)4037951-6 gnd
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title	Fundamentals of mathematical logic
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title_full	Fundamentals of mathematical logic Peter G. Hinman
title_fullStr	Fundamentals of mathematical logic Peter G. Hinman
title_full_unstemmed	Fundamentals of mathematical logic Peter G. Hinman
title_short	Fundamentals of mathematical logic
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topic	Lógica matemática (textos avançados) larpcal Wiskundige logica gtt Logic, Symbolic and mathematical Model theory Set theory Recursion theory Mathematische Logik (DE-588)4037951-6 gnd
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