Model theory and its applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston, Mass.
Allyn and Bacon
1972
|
| Series: | Allyn and Bacon series in advanced mathematics.
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 333 S. Ill. |
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Record in the Search Index
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| adam_text | Contents
INTRODUCTION AND PREREQUISITES 1
1. CLASSICAL WORK 6
1.1 Structures 6
1.2 Language and Truth 12
1.3 Elementary Classes 25
1.4 The Lowenheim-Skolem Theorem 28
1.5 Compactness 38
1.6 Elementary Equivalence and Complete Theories 47
1.7 Elementary Extensions and Model-Completeness 56
1.8 Real-Closed Fields 66
2. ULTRAPRODUCTS 74
2.1 Definition of Ultraproducts 74
2.2 Further Properties and Examples 84
2.3 Set-Theoretic Relations; Regular Ultraproducts 90
2.4 Ultralimits 98
2.5 Algebraic Characterization of Elementary Classes 119
2.6 Limit Ultraproducts 125
2.7 Saturated Models 138
2.8 Special Models 141
3. RELATIONSHIPS WITH LOGIC 154
3.1 Proofs 154
3.2 The Completeness Theorems I6l
vii
viii Contents
4. AN APPLICATION TO ALGEBRA 168
4.1 Valued Fields 168
4.2 Artin s Conjecture 183
4.3 The Basic Ax-Kochen Results 202
4.4 Further Results of Ax and Kochen 209
5. APPLICATIONS TO ANALYSIS 227
5.1 Ultrapowers of the Reals 227
5.2 nonstandard analysis on the reals 233
5.3 Functions of Several Real Variables;
Complex Numbers 254
5.4 Complex Analysis 275
5.5 The Bernstein-Robinson Theorem 307
BIBLIOGRAPHY 322
APPENDIX: GLOSSARY OF SYMBOLS 326
INDEX 331
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| indexdate | 2024-07-09T15:38:10Z |
| institution | BVB |
| language | English |
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| physical | X, 333 S. Ill. |
| publishDate | 1972 |
| publishDateSearch | 1972 |
| publishDateSort | 1972 |
| publisher | Allyn and Bacon |
| record_format | marc |
| series2 | Allyn and Bacon series in advanced mathematics. |
| spelling | Kopperman, Ralph Verfasser aut Model theory and its applications Boston, Mass. Allyn and Bacon 1972 X, 333 S. Ill. txt rdacontent n rdamedia nc rdacarrier Allyn and Bacon series in advanced mathematics. Modèles, Théorie des Modèles, Théorie des ram Model theory Modelltheorie (DE-588)4114617-7 gnd rswk-swf Modelltheorie (DE-588)4114617-7 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001286369&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kopperman, Ralph Model theory and its applications Modèles, Théorie des Modèles, Théorie des ram Model theory Modelltheorie (DE-588)4114617-7 gnd |
| subject_GND | (DE-588)4114617-7 |
| title | Model theory and its applications |
| title_auth | Model theory and its applications |
| title_exact_search | Model theory and its applications |
| title_full | Model theory and its applications |
| title_fullStr | Model theory and its applications |
| title_full_unstemmed | Model theory and its applications |
| title_short | Model theory and its applications |
| title_sort | model theory and its applications |
| topic | Modèles, Théorie des Modèles, Théorie des ram Model theory Modelltheorie (DE-588)4114617-7 gnd |
| topic_facet | Modèles, Théorie des Model theory Modelltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001286369&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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