Mathematical logic:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg ; New York
Springer
1996
|
| Edition: | 2. ed., corr. 2. printing |
| Series: | Undergraduate texts in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 277 - 279 |
| Physical Description: | X, 289 S. graph. Darst. |
| ISBN: | 3540942580 0387942580 |
Staff View
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Record in the Search Index
| _version_ | 1804138151514472448 |
|---|---|
| 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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| author_facet | Ebbinghaus, Heinz-Dieter 1939- Flum, Jörg 1944- Thomas, Wolfgang 1947- |
| author_role | aut aut aut |
| author_sort | Ebbinghaus, Heinz-Dieter 1939- |
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| callnumber-raw | QA9.E2213 1994 |
| callnumber-search | QA9.E2213 1994 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 130 |
| ctrlnum | (OCoLC)722636259 (DE-599)BVBBV023513347 |
| dewey-full | 511.320 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 20 |
| dewey-search | 511.3 20 |
| dewey-sort | 3511.3 220 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. ed., corr. 2. printing |
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| index_date | 2024-07-02T22:31:30Z |
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| isbn | 3540942580 0387942580 |
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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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