A concise introduction to mathematical logic:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English German |
| Published: |
New York
Springer
2006
|
| Edition: | 2. ed. |
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (S. 241-246) and index |
| Physical Description: | XVII, 256 S. Ill., graph. Darst. |
| ISBN: | 0387302948 9780387302942 |
Staff View
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| 245 | 1 | 0 | |a A concise introduction to mathematical logic |c Wolfgang Rautenberg |
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Record in the Search Index
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| adam_text | WOLFGANG RAUTENBERG A CONCISE INTRODUCTION TO MATHEMATICAL LOGIC SECOND
EDITION 4Y SPRINGER CONTENTS INTRODUCTION XNI NOTATION XVI 1
PROPOSITIONAL LOGIC 1 1.1 BOOLEAN FUNCTIONS AND FORMULAS 2 1.2 SEMANTIC
EQUIVALENCE AND NORMAL FORMS 9 1.3 TAUTOLOGIES AND LOGICAL CONSEQUENCE
14 1.4 A COMPLETE CALCULUS FOR 1 = 18 1.5 APPLICATIONS OF THE
COMPACTNESS THEOREM 25 1.6 HILBERT CALCULI 29 2 PREDICATE LOGIC 33 2.1
MATHEMATICAL STRUCTURES 34 2.2 SYNTAX OF ELEMENTARY LANGUAGES 43 2.3
SEMANTICS OF ELEMENTARY LANGUAGES 49 2.4 GENERAL VALIDITY AND LOGICAL
EQUIVALENCE 58 2.5 LOGICAL CONSEQUENCE AND THEORIES 62 2.6 EXPLICIT
DEFINITIONS*EXPANDING LANGUAGES 67 3 GODEL S COMPLETENESS THEOREM 71 3.1
A CALCULUS OF NATURAL DEDUCTION 72 3.2 THE COMPLETENESS PROOF 76 3.3
FIRST APPLICATIONS*NONSTANDARD MODELS 81 3.4 ZFC AND SKOLEM S PARADOX 87
3.5 ENUMERABILITY AND DECIDABILITY 92 3.6 COMPLETE HILBERT CALCULI 95
3.7 FIRST-ORDER FRAGMENTS AND EXTENSIONS 99 4 THE FOUNDATIONS OF LOGIC
PROGRAMMING 105 4.1 TERM MODELS AND HORN FORMULAS 106 4.2 PREPOSITIONAL
RESOLUTION 112 4.3 UNIFICATION 119 4.4 LOGIC PROGRAMMING 122 4.5 PROOF
OF THE MAIN THEOREM 129 5 ELEMENTS OF MODEL THEORY 131 5.1 ELEMENTARY
EXTENSIONS 132 5.2 COMPLETE AND K-CATEGORICAL THEORIES 137 5.3
EHRENFEUCHT S GAME 142 5.4 EMBEDDING AND CHARACTERIZATION THEOREMS 145
5.5 MODEL COMPLETENESS 151 5.6 QUANTIFIER ELIMINATION 157 5.7 REDUCED
PRODUCTS AND ULTRAPRODUCTS 163 6 INCOMPLETENESS AND UNDECIDABILITY 167
6.1 RECURSIVE AND PRIMITIVE RECURSIVE FUNCTIONS 169 6.2 ARITHMETIZATION
176 6.3 REPRESENTABILITY OF ARITHMETICAL PREDICATES 182 6.4 THE
REPRESENTABILITY THEOREM 189 6.5 THE THEOREMS OF GODEL, TARSKI, CHURCH
194 6.6 TRANSFER BY INTERPRETATION ... .... 200 6.7 THE ARITHMETICAL
HIERARCHY 205 7 ON THE THEORY OF SELF-REFERENCE 209 7.1 THE DERIVABILITY
CONDITIONS 210 7.2 THE THEOREMS OF GODEL AND LOB 217 7.3 THE PROVABILITY
LOGIC G *, 221 7.4 THE MODAL TREATMENT OF SELF-REFERENCE 223 7.5 A
BIMODAL PROVABILITY LOGIC FOR PA 226 7.6 MODAL OPERATORS IN ZFC 228
HINTS TO THE EXERCISES 231 LITERATURE 241 INDEX OF TERMS AND NAMES 247
INDEX OF SYMBOLS 255
|
| adam_txt |
WOLFGANG RAUTENBERG A CONCISE INTRODUCTION TO MATHEMATICAL LOGIC SECOND
EDITION 4Y SPRINGER CONTENTS INTRODUCTION XNI NOTATION XVI 1
PROPOSITIONAL LOGIC 1 1.1 BOOLEAN FUNCTIONS AND FORMULAS 2 1.2 SEMANTIC
EQUIVALENCE AND NORMAL FORMS 9 1.3 TAUTOLOGIES AND LOGICAL CONSEQUENCE
14 1.4 A COMPLETE CALCULUS FOR 1 = 18 1.5 APPLICATIONS OF THE
COMPACTNESS THEOREM 25 1.6 HILBERT CALCULI 29 2 PREDICATE LOGIC 33 2.1
MATHEMATICAL STRUCTURES 34 2.2 SYNTAX OF ELEMENTARY LANGUAGES' 43 2.3
SEMANTICS OF ELEMENTARY LANGUAGES 49 2.4 GENERAL VALIDITY AND LOGICAL
EQUIVALENCE 58 2.5 LOGICAL CONSEQUENCE AND THEORIES 62 2.6 EXPLICIT
DEFINITIONS*EXPANDING LANGUAGES 67 3 GODEL'S COMPLETENESS THEOREM 71 3.1
A CALCULUS OF NATURAL DEDUCTION 72 3.2 THE COMPLETENESS PROOF 76 3.3
FIRST APPLICATIONS*NONSTANDARD MODELS 81 3.4 ZFC AND SKOLEM'S PARADOX 87
3.5 ENUMERABILITY AND DECIDABILITY 92 3.6 COMPLETE HILBERT CALCULI 95
3.7 FIRST-ORDER FRAGMENTS AND EXTENSIONS 99 4 THE FOUNDATIONS OF LOGIC
PROGRAMMING 105 4.1 TERM MODELS AND HORN FORMULAS 106 4.2 PREPOSITIONAL
RESOLUTION 112 4.3 UNIFICATION 119 4.4 LOGIC PROGRAMMING 122 4.5 PROOF
OF THE MAIN THEOREM 129 5 ELEMENTS OF MODEL THEORY 131 5.1 ELEMENTARY
EXTENSIONS 132 5.2 COMPLETE AND K-CATEGORICAL THEORIES 137 5.3
EHRENFEUCHT'S GAME 142 5.4 EMBEDDING AND CHARACTERIZATION THEOREMS 145
5.5 MODEL COMPLETENESS 151 5.6 QUANTIFIER ELIMINATION 157 5.7 REDUCED
PRODUCTS AND ULTRAPRODUCTS 163 6 INCOMPLETENESS AND UNDECIDABILITY 167
6.1 RECURSIVE AND PRIMITIVE RECURSIVE FUNCTIONS 169 6.2 ARITHMETIZATION
176 6.3 REPRESENTABILITY OF ARITHMETICAL PREDICATES 182 6.4 THE
REPRESENTABILITY THEOREM 189 6.5 THE THEOREMS OF GODEL, TARSKI, CHURCH
194 6.6 TRANSFER BY INTERPRETATION .'.'" 200 6.7 THE ARITHMETICAL
HIERARCHY 205 7 ON THE THEORY OF SELF-REFERENCE 209 7.1 THE DERIVABILITY
CONDITIONS 210 7.2 THE THEOREMS OF GODEL AND LOB 217 7.3 THE PROVABILITY
LOGIC G *, 221 7.4 THE MODAL TREATMENT OF SELF-REFERENCE 223 7.5 A
BIMODAL PROVABILITY LOGIC FOR PA 226 7.6 MODAL OPERATORS IN ZFC 228
HINTS TO THE EXERCISES 231 LITERATURE 241 INDEX OF TERMS AND NAMES 247
INDEX OF SYMBOLS 255 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Rautenberg, Wolfgang |
| author_facet | Rautenberg, Wolfgang |
| author_role | aut |
| author_sort | Rautenberg, Wolfgang |
| author_variant | w r wr |
| building | Verbundindex |
| bvnumber | BV021827699 |
| callnumber-first | Q - Science |
| callnumber-label | QA9 |
| callnumber-raw | QA9 |
| callnumber-search | QA9 |
| callnumber-sort | QA 19 |
| callnumber-subject | QA - Mathematics |
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| ctrlnum | (OCoLC)66527737 (DE-599)BVBBV021827699 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. ed. |
| format | Book |
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| series2 | Universitext |
| spelling | Rautenberg, Wolfgang Verfasser aut Einführung in die mathematische Logik A concise introduction to mathematical logic Wolfgang Rautenberg 2. ed. New York Springer 2006 XVII, 256 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Includes bibliographical references (S. 241-246) and index Mathematik Logic, Symbolic and mathematical Mathematics Stufe 1 (DE-588)4362503-4 gnd rswk-swf Prädikatenlogik (DE-588)4046974-8 gnd rswk-swf Gödelscher Unvollständigkeitssatz (DE-588)4021417-5 gnd rswk-swf Modelltheorie (DE-588)4114617-7 gnd rswk-swf Unentscheidbarkeit (DE-588)4294363-2 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Aussagenlogik (DE-588)4136098-9 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Mathematische Logik (DE-588)4037951-6 s DE-604 Prädikatenlogik (DE-588)4046974-8 s Stufe 1 (DE-588)4362503-4 s Unentscheidbarkeit (DE-588)4294363-2 s 1\p DE-604 Aussagenlogik (DE-588)4136098-9 s 2\p DE-604 Gödelscher Unvollständigkeitssatz (DE-588)4021417-5 s 3\p DE-604 Modelltheorie (DE-588)4114617-7 s 4\p DE-604 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2696666&prov=M&dok_var=1&dok_ext=htm Inhaltstext HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015039737&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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Rautenberg, Wolfgang A concise introduction to mathematical logic Mathematik Logic, Symbolic and mathematical Mathematics Stufe 1 (DE-588)4362503-4 gnd Prädikatenlogik (DE-588)4046974-8 gnd Gödelscher Unvollständigkeitssatz (DE-588)4021417-5 gnd Modelltheorie (DE-588)4114617-7 gnd Unentscheidbarkeit (DE-588)4294363-2 gnd Mathematische Logik (DE-588)4037951-6 gnd Aussagenlogik (DE-588)4136098-9 gnd |
| subject_GND | (DE-588)4362503-4 (DE-588)4046974-8 (DE-588)4021417-5 (DE-588)4114617-7 (DE-588)4294363-2 (DE-588)4037951-6 (DE-588)4136098-9 (DE-588)4123623-3 |
| title | A concise introduction to mathematical logic |
| title_alt | Einführung in die mathematische Logik |
| title_auth | A concise introduction to mathematical logic |
| title_exact_search | A concise introduction to mathematical logic |
| title_exact_search_txtP | A concise introduction to mathematical logic |
| title_full | A concise introduction to mathematical logic Wolfgang Rautenberg |
| title_fullStr | A concise introduction to mathematical logic Wolfgang Rautenberg |
| title_full_unstemmed | A concise introduction to mathematical logic Wolfgang Rautenberg |
| title_short | A concise introduction to mathematical logic |
| title_sort | a concise introduction to mathematical logic |
| topic | Mathematik Logic, Symbolic and mathematical Mathematics Stufe 1 (DE-588)4362503-4 gnd Prädikatenlogik (DE-588)4046974-8 gnd Gödelscher Unvollständigkeitssatz (DE-588)4021417-5 gnd Modelltheorie (DE-588)4114617-7 gnd Unentscheidbarkeit (DE-588)4294363-2 gnd Mathematische Logik (DE-588)4037951-6 gnd Aussagenlogik (DE-588)4136098-9 gnd |
| topic_facet | Mathematik Logic, Symbolic and mathematical Mathematics Stufe 1 Prädikatenlogik Gödelscher Unvollständigkeitssatz Modelltheorie Unentscheidbarkeit Mathematische Logik Aussagenlogik Lehrbuch |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2696666&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015039737&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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