Verfügbarkeit: Mathematical logic

Mathematical logic:

Gespeichert in:

Bibliographische Detailangaben
Hauptverfasser:	Ebbinghaus, Heinz-Dieter 1939- (VerfasserIn), Flum, Jörg 1944- (VerfasserIn), Thomas, Wolfgang 1947- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Berlin ; Heidelberg ; New York Springer 1996
Ausgabe:	2. ed., corr. 2. printing
Schriftenreihe:	Undergraduate texts in mathematics
Schlagworte:	Logic, Symbolic and mathematical Mathematische Logik Einführung Lehrbuch
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	Literaturverz. S. 277 - 279
Beschreibung:	X, 289 S. graph. Darst.
ISBN:	3540942580 0387942580

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Datensatz im Suchindex

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adam_text	H.-D. EBBINGHAUS J. FLUM W. THOMAS MATHEMATICAL LOGIC SECOND EDITION WITH 13 ILLUSTRATIONS SPRINGEI CONTENTS PREFACE V PART A 1 I INTRODUCTION 3 §1. AN EXAMPLE FROM GROUP THEORY 4 §2. AN EXAMPLE FROM THE THEORY OF EQUIVALENCE RELATIONS ... 5 §3. A PRELIMINARY ANALYSIS 6 §4. PREVIEW 8 II SYNTAX OF FIRST-ORDER LANGUAGES * 11 §1. ALPHABETS 11 §2. THE ALPHABET OF A FIRST-ORDER LANGUAGE 13 §3. TERMS AND FORMULAS IN FIRST-ORDER LANGUAGES 15 §4. INDUCTION IN THE CALCULUS OF TERMS AND IN THE CALCULUS OF FORMULAS 19 §5. FREE VARIABLES AND SENTENCES 24 III SEMANTICS OF FIRST-ORDER LANGUAGES 27 §1. STRUCTURES AND INTERPRETATIONS 28 §2. STANDARDIZATION OF CONNECTIVES 31 §3. THE SATISFACTION RELATION 32 §4. THE CONSEQUENCE RELATION 33 §5. TWO LEMMAS ON THE SATISFACTION RELATION 40 §6. SOME SIMPLE FORMALIZATIONS 44 §7. SOME REMARKS ON FORMALIZABILITY 48 §8. SUBSTITUTION 52 VIII CONTENTS IV A SEQUENT CALCULUS 59 §1. SEQUENT RULES 60 §2. STRUCTURAL RULES AND CONNECTIVE RULES 62 §3. DERIVABLE CONNECTIVE RULES 63 §4. QUANTIFIER AND EQUALITY RULES 66 §5. FURTHER DERIVABLE RULES AND SEQUENTS 68 §6. SUMMARY AND EXAMPLE 69 §7. CONSISTENCY 72 V THE COMPLETENESS THEOREM 75 §1. HENKIN S THEOREM 75 §2. SATISFIABILITY OF CONSISTENT SETS OF FORMULAS (THE COUNTABLE CASE) 79 §3. SATISFIABILITY OF CONSISTENT SETS OF FORMULAS (THE GENERAL CASE) 82 §4. THE COMPLETENESS THEOREM 85 VI THE LOWENHEIM-SKOLEM AND THE COMPACTNESS THEOREM 87 §1. THE LOWENHEIM-SKOLEM THEOREM 87 §2. THE COMPACTNESS THEOREM 88 §3. ELEMENTARY CLASSES 91 §4. ELEMENTARILY EQUIVALENT STRUCTURES 94 VII THE SCOPE OF FIRST-ORDER LOGIC 99 §1. THE NOTION OF FORMAL PROOF 99 §2. MATHEMATICS WITHIN THE FRAMEWORK OF FIRST-ORDER LOGIC . 103 §3. THE ZERMELO-FRAENKEL AXIOMS FOR SET THEORY 107 §4. SET THEORY AS A BASIS FOR MATHEMATICS 110 VIII SYNTACTIC INTERPRETATIONS AND NORMAL FORMS 115 §1. TERM-REDUCED FORMULAS AND RELATIONAL SYMBOL SETS . . . . 115 §2. SYNTACTIC INTERPRETATIONS 118 §3. EXTENSIONS BY DEFINITIONS 125 §4. NORMAL FORMS 128 CONTENTS IX PART B 135 IX EXTENSIONS OF FIRST-ORDER LOGIC 137 §1. SECOND-ORDER LOGIC 138 §2. THE SYSTEM C ULU 142 §3. THE SYSTEM C Q 148 X LIMITATIONS OF THE FORMAL METHOD 151 §1. DECIDABILITY AND ENUMERABILITY 152 §2. REGISTER MACHINES 157 §3. THE HALTING PROBLEM FOR REGISTER MACHINES 163 §4. THE UNDECIDABILITY OF FIRST-ORDER LOGIC 167 §5. TRAHTENBROT S THEOREM AND THE INCOMPLETENESS OF SECOND- ORDER LOGIC 170 §6. THEORIES AND DECIDABILITY 173 §7. SELF-REFERENTIAL STATEMENTS AND GODEL S INCOMPLETENESS THEOREMS 181 XI FREE MODELS AND LOGIC PROGRAMMING 189 §1. HERBRAND S THEOREM 189 §2. FREE MODELS AND UNIVERSAL HORN FORMULAS 193 §3. HERBRAND STRUCTURES 198 §4. PREPOSITIONAL LOGIC 200 §5. PREPOSITIONAL RESOLUTION 207 §6. FIRST-ORDER RESOLUTION (WITHOUT UNIFICATION) 218 §7. LOGIC PROGRAMMING 226 XII AN ALGEBRAIC CHARACTERIZATION OF ELEMENTARY EQUIVA- LENCE 243 §1. FINITE AND PARTIAL ISOMORPHISMS 244 §2. FRAISSE S THEOREM 249 §3. PROOF OF FRA ISSE S THEOREM 251 §4. EHRENFEUCHT GAMES 258 X CONTENTS XIII LINDSTROM S THEOREMS 261 §1. LOGICAL SYSTEMS 261 §2. COMPACT REGULAR LOGICAL SYSTEMS 264 §3. LINDSTROM S FIRST THEOREM 266 §4. LINDSTROM S SECOND THEOREM 272 REFERENCES 277 SYMBOL INDEX 280 SUBJECT INDEX 283
adam_txt	H.-D. EBBINGHAUS J. FLUM W. THOMAS MATHEMATICAL LOGIC SECOND EDITION WITH 13 ILLUSTRATIONS SPRINGEI CONTENTS PREFACE V PART A 1 I INTRODUCTION 3 §1. AN EXAMPLE FROM GROUP THEORY 4 §2. AN EXAMPLE FROM THE THEORY OF EQUIVALENCE RELATIONS . 5 §3. A PRELIMINARY ANALYSIS 6 §4. PREVIEW 8 II SYNTAX OF FIRST-ORDER LANGUAGES * 11 §1. ALPHABETS 11 §2. THE ALPHABET OF A FIRST-ORDER LANGUAGE 13 §3. TERMS AND FORMULAS IN FIRST-ORDER LANGUAGES 15 §4. INDUCTION IN THE CALCULUS OF TERMS AND IN THE CALCULUS OF FORMULAS 19 §5. FREE VARIABLES AND SENTENCES 24 III SEMANTICS OF FIRST-ORDER LANGUAGES 27 §1. STRUCTURES AND INTERPRETATIONS 28 §2. STANDARDIZATION OF CONNECTIVES 31 §3. THE SATISFACTION RELATION 32 §4. THE CONSEQUENCE RELATION 33 §5. TWO LEMMAS ON THE SATISFACTION RELATION 40 §6. SOME SIMPLE FORMALIZATIONS 44 §7. SOME REMARKS ON FORMALIZABILITY 48 §8. SUBSTITUTION 52 VIII CONTENTS IV A SEQUENT CALCULUS 59 §1. SEQUENT RULES 60 §2. STRUCTURAL RULES AND CONNECTIVE RULES 62 §3. DERIVABLE CONNECTIVE RULES 63 §4. QUANTIFIER AND EQUALITY RULES 66 §5. FURTHER DERIVABLE RULES AND SEQUENTS 68 §6. SUMMARY AND EXAMPLE 69 §7. CONSISTENCY 72 V THE COMPLETENESS THEOREM 75 §1. HENKIN'S THEOREM 75 §2. SATISFIABILITY OF CONSISTENT SETS OF FORMULAS (THE COUNTABLE CASE) 79 §3. SATISFIABILITY OF CONSISTENT SETS OF FORMULAS (THE GENERAL CASE) 82 §4. THE COMPLETENESS THEOREM 85 VI THE LOWENHEIM-SKOLEM AND THE COMPACTNESS THEOREM 87 §1. THE LOWENHEIM-SKOLEM THEOREM 87 §2. THE COMPACTNESS THEOREM 88 §3. ELEMENTARY CLASSES 91 §4. ELEMENTARILY EQUIVALENT STRUCTURES 94 VII THE SCOPE OF FIRST-ORDER LOGIC 99 §1. THE NOTION OF FORMAL PROOF 99 §2. MATHEMATICS WITHIN THE FRAMEWORK OF FIRST-ORDER LOGIC . 103 §3. THE ZERMELO-FRAENKEL AXIOMS FOR SET THEORY 107 §4. SET THEORY AS A BASIS FOR MATHEMATICS 110 VIII SYNTACTIC INTERPRETATIONS AND NORMAL FORMS 115 §1. TERM-REDUCED FORMULAS AND RELATIONAL SYMBOL SETS . . . . 115 §2. SYNTACTIC INTERPRETATIONS 118 §3. EXTENSIONS BY DEFINITIONS 125 §4. NORMAL FORMS 128 CONTENTS IX PART B 135 IX EXTENSIONS OF FIRST-ORDER LOGIC 137 §1. SECOND-ORDER LOGIC 138 §2. THE SYSTEM C ULU 142 §3. THE SYSTEM C Q 148 X LIMITATIONS OF THE FORMAL METHOD 151 §1. DECIDABILITY AND ENUMERABILITY 152 §2. REGISTER MACHINES 157 §3. THE HALTING PROBLEM FOR REGISTER MACHINES 163 §4. THE UNDECIDABILITY OF FIRST-ORDER LOGIC 167 §5. TRAHTENBROT'S THEOREM AND THE INCOMPLETENESS OF SECOND- ORDER LOGIC 170 §6. THEORIES AND DECIDABILITY 173 §7. SELF-REFERENTIAL STATEMENTS AND GODEL'S INCOMPLETENESS THEOREMS 181 XI FREE MODELS AND LOGIC PROGRAMMING 189 §1. HERBRAND'S THEOREM 189 §2. FREE MODELS AND UNIVERSAL HORN FORMULAS 193 §3. HERBRAND STRUCTURES 198 §4. PREPOSITIONAL LOGIC 200 §5. PREPOSITIONAL RESOLUTION 207 §6. FIRST-ORDER RESOLUTION (WITHOUT UNIFICATION) 218 §7. LOGIC PROGRAMMING 226 XII AN ALGEBRAIC CHARACTERIZATION OF ELEMENTARY EQUIVA- LENCE 243 §1. FINITE AND PARTIAL ISOMORPHISMS 244 §2. FRAISSE'S THEOREM 249 §3. PROOF OF FRA'ISSE'S THEOREM 251 §4. EHRENFEUCHT GAMES 258 X CONTENTS XIII LINDSTROM'S THEOREMS 261 §1. LOGICAL SYSTEMS 261 §2. COMPACT REGULAR LOGICAL SYSTEMS 264 §3. LINDSTROM'S FIRST THEOREM 266 §4. LINDSTROM'S SECOND THEOREM 272 REFERENCES 277 SYMBOL INDEX 280 SUBJECT INDEX 283
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author	Ebbinghaus, Heinz-Dieter 1939- Flum, Jörg 1944- Thomas, Wolfgang 1947-
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spelling	Ebbinghaus, Heinz-Dieter 1939- Verfasser (DE-588)107046857 aut Einführung in die mathematische Logik Mathematical logic H.-D. Ebbinghaus ; J. Flum ; W. Thomas 2. ed., corr. 2. printing Berlin ; Heidelberg ; New York Springer 1996 X, 289 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Literaturverz. S. 277 - 279 Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content 2\p (DE-588)4123623-3 Lehrbuch gnd-content Mathematische Logik (DE-588)4037951-6 s DE-604 Flum, Jörg 1944- Verfasser (DE-588)121343391 aut Thomas, Wolfgang 1947- Verfasser (DE-588)137276346 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016834627&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Ebbinghaus, Heinz-Dieter 1939- Flum, Jörg 1944- Thomas, Wolfgang 1947- Mathematical logic Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd
subject_GND	(DE-588)4037951-6 (DE-588)4151278-9 (DE-588)4123623-3
title	Mathematical logic
title_alt	Einführung in die mathematische Logik
title_auth	Mathematical logic
title_exact_search	Mathematical logic
title_exact_search_txtP	Mathematical logic
title_full	Mathematical logic H.-D. Ebbinghaus ; J. Flum ; W. Thomas
title_fullStr	Mathematical logic H.-D. Ebbinghaus ; J. Flum ; W. Thomas
title_full_unstemmed	Mathematical logic H.-D. Ebbinghaus ; J. Flum ; W. Thomas
title_short	Mathematical logic
title_sort	mathematical logic
topic	Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd
topic_facet	Logic, Symbolic and mathematical Mathematische Logik Einführung Lehrbuch
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016834627&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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