Introduction to model theory and to the metamathematics of algebra:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
North-Holland Publ [u.a.]
1974
|
| Ausgabe: | 2., rev. print. |
| Schriftenreihe: | Studies in logic and the foundations of mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 284 S. |
| ISBN: | 0444106715 0720422221 |
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| 245 | 1 | 0 | |a Introduction to model theory and to the metamathematics of algebra |c Abraham Robinson |
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| 264 | 1 | |a Amsterdam |b North-Holland Publ [u.a.] |c 1974 | |
| 300 | |a IX, 284 S. | ||
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Datensatz im Suchindex
| _version_ | 1804135840540000256 |
|---|---|
| adam_text | LIST OF CONTENTS
CHAPTER I
THE LOWER PREDICATE CALCULUS
1.1. General introduction 1
1.2. Rules of formation 3
1.3. Rules of deduction 6
1.4. Semantic interpretation 9
1.5. The relation between deductive and descriptive concepts 11
1.6. Sets of sentences and their varieties 20
1.7. Problems 22
CHAPTER II
ALGEBRAIC THEORIES
2.1. Equality 23
2.2. Specification of axiomatic systems 25
2.3. Related sets of sentences 31
2.4. Embedding theorems and transfer principles 34
2.5. Malcev s theory of normal chains 45
2.6. Problems 49
CHAPTER III
SOME CONCEPTS AND METHODS OF MODEL THEORY
3.1. Skolem functions; relativization 51
3.2. The extension of models 54
3.3. The prefix problem 65
3.4. Ohstructions to elementary extension 75
3.5. Convex systems 80
3.6. Model consistency 84
3.7. Problems 86
CHAPTER IV
COMPLETENESS
4.1. A test for completeness 88
4.2. Model completeness 91
4.3. Relative model completeness 105
4.4. Problems 110
vn
Vm LIST OF CONTENTS
CHAPTER V
DEFINABILITY
5.1. The consistency lemma 112
5.2. Beth s theorem 117
5.3. Relative definitions 119
5.4. Application to the Nullstellensatz 125
5.5. Model completion 128
5.6. Problems 137
CHAPTER VI
GENERALIZATION OF ALGEBRAIC CONCEPTS
6.1. Polynomials in general axiomatic systems 139
6.2. Bounded predicates 149
6.3. Algebraic predicates 154
6.4. Algebraic predicates and convex systems 161
6.5. Separability 167
6.6. Problems 171
CHAPTER VII
METAMATHEMATICAL THEORY OF IDEALS
7.1. Introduction 172
7.2. Metamathematical ideals 173
7.3. Connection between ideals in different domains 175
7.4. Disjunctive ideals 179
7.5. Ideals and homomorphisms 185
7.6. Problems 191
CHAPTER VIII
METAMATHEMATICAL THEORY OF VARIETIES
8.1. Varieties of structures 192
8.2. Pre ideals and their varieties 200
8.3. Metamathematical varieties and algebraic varieties 204
8.4. Differential ideals 209
8.5. Hilbert s seventeenth problem 214
8.6. Problems 224
CHAPTER IX
SELECTED TOPICS
9.1. Introduction of function symbols 226
9.2. The elimination of quantifiers 231
LIST OF CONTENTS IX
9.3. Direct products and ultraproducts 238
9.4. Non standard analysis 244
9.5. Non standard theory of functions of a real variable 252
9.6. Non standard analysis of functions of several variables 261
9.7. Problems 270
Bibliography 272
Index of Authors 281
Subject Index 283
|
| adam_txt |
LIST OF CONTENTS
CHAPTER I
THE LOWER PREDICATE CALCULUS
1.1. General introduction 1
1.2. Rules of formation 3
1.3. Rules of deduction 6
1.4. Semantic interpretation 9
1.5. The relation between deductive and descriptive concepts 11
1.6. Sets of sentences and their varieties 20
1.7. Problems 22
CHAPTER II
ALGEBRAIC THEORIES
2.1. Equality 23
2.2. Specification of axiomatic systems 25
2.3. Related sets of sentences 31
2.4. Embedding theorems and transfer principles 34
2.5. Malcev's theory of normal chains 45
2.6. Problems 49
CHAPTER III
SOME CONCEPTS AND METHODS OF MODEL THEORY
3.1. Skolem functions; relativization 51
3.2. The extension of models 54
3.3. The prefix problem 65
3.4. Ohstructions to elementary extension 75
3.5. Convex systems 80
3.6. Model consistency 84
3.7. Problems 86
CHAPTER IV
COMPLETENESS
4.1. A test for completeness 88
4.2. Model completeness 91
4.3. Relative model completeness 105
4.4. Problems 110
vn
Vm LIST OF CONTENTS
CHAPTER V
DEFINABILITY
5.1. The consistency lemma 112
5.2. Beth's theorem 117
5.3. Relative definitions 119
5.4. Application to the Nullstellensatz 125
5.5. Model completion 128
5.6. Problems 137
CHAPTER VI
GENERALIZATION OF ALGEBRAIC CONCEPTS
6.1. Polynomials in general axiomatic systems 139
6.2. Bounded predicates 149
6.3. Algebraic predicates 154
6.4. Algebraic predicates and convex systems 161
6.5. Separability 167
6.6. Problems 171
CHAPTER VII
METAMATHEMATICAL THEORY OF IDEALS
7.1. Introduction 172
7.2. Metamathematical ideals 173
7.3. Connection between ideals in different domains 175
7.4. Disjunctive ideals 179
7.5. Ideals and homomorphisms 185
7.6. Problems 191
CHAPTER VIII
METAMATHEMATICAL THEORY OF VARIETIES
8.1. Varieties of structures 192
8.2. Pre ideals and their varieties 200
8.3. Metamathematical varieties and algebraic varieties 204
8.4. Differential ideals 209
8.5. Hilbert's seventeenth problem 214
8.6. Problems 224
CHAPTER IX
SELECTED TOPICS
9.1. Introduction of function symbols 226
9.2. The elimination of quantifiers 231
LIST OF CONTENTS IX
9.3. Direct products and ultraproducts 238
9.4. Non standard analysis 244
9.5. Non standard theory of functions of a real variable 252
9.6. Non standard analysis of functions of several variables 261
9.7. Problems 270
Bibliography 272
Index of Authors 281
Subject Index 283 |
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| spelling | Robinson, Abraham Verfasser aut Introduction to model theory and to the metamathematics of algebra Abraham Robinson 2., rev. print. Amsterdam North-Holland Publ [u.a.] 1974 IX, 284 S. txt rdacontent n rdamedia nc rdacarrier Studies in logic and the foundations of mathematics Modelltheorie (DE-588)4114617-7 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Metamathematik (DE-588)4074759-1 gnd rswk-swf Theorie (DE-588)4059787-8 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Modelltheorie (DE-588)4114617-7 s Mathematik (DE-588)4037944-9 s 2\p DE-604 Algebra (DE-588)4001156-2 s Theorie (DE-588)4059787-8 s 3\p DE-604 Metamathematik (DE-588)4074759-1 s 4\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015111094&sequence=000002&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 | Robinson, Abraham Introduction to model theory and to the metamathematics of algebra Modelltheorie (DE-588)4114617-7 gnd Algebra (DE-588)4001156-2 gnd Mathematik (DE-588)4037944-9 gnd Metamathematik (DE-588)4074759-1 gnd Theorie (DE-588)4059787-8 gnd |
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| title | Introduction to model theory and to the metamathematics of algebra |
| title_auth | Introduction to model theory and to the metamathematics of algebra |
| title_exact_search | Introduction to model theory and to the metamathematics of algebra |
| title_exact_search_txtP | Introduction to model theory and to the metamathematics of algebra |
| title_full | Introduction to model theory and to the metamathematics of algebra Abraham Robinson |
| title_fullStr | Introduction to model theory and to the metamathematics of algebra Abraham Robinson |
| title_full_unstemmed | Introduction to model theory and to the metamathematics of algebra Abraham Robinson |
| title_short | Introduction to model theory and to the metamathematics of algebra |
| title_sort | introduction to model theory and to the metamathematics of algebra |
| topic | Modelltheorie (DE-588)4114617-7 gnd Algebra (DE-588)4001156-2 gnd Mathematik (DE-588)4037944-9 gnd Metamathematik (DE-588)4074759-1 gnd Theorie (DE-588)4059787-8 gnd |
| topic_facet | Modelltheorie Algebra Mathematik Metamathematik Theorie Einführung |
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