Mathematical logic and model theory: a brief introduction
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Springer
2011
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 193 S. |
| ISBN: | 9781447121756 |
Staff View
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Record in the Search Index
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| adam_text | Contents Introduction..................................................................................................... 1 1 First-Order Logic..................................................................................... 1.1 Analysis of Mathematical Proofs....................................................... 1.2 Construction of Formal Languages................................................... 1.3 Formal Proofs ................................................................................... 1.4 Completeness of First-Order Logic................................................... 1.5 First-Order Semantics........................................................................ 1.6 Axiomatization of Several Mathematical Theories.......................... 1.7 Exercises for Chapter 1...................................................................... 5 5 8 14 25 36 46 56 2 Model Constructions............................................................................... 2.1 Term Models..................................................................................... 2.2 Morphisms of Structures .................................................................. 2.3 Substructures..................................................................................... 2.4 Elementary Extensions and Chains................................................... 2.5 Saturated Structures ......................................................................... 2.6 Ultraproducts..................................................................................... 2.7 Exercises
for Chapter 2..................................................................... 61 62 65 70 75 80 88 97 3 Properties of Model Classes..................................................................... 101 3.1 Compactness and Separation..............................................................101 3.2 Categoricity........................................................................................ 106 3.3 Model Completeness...........................................................................Ill 3.4 Quantifier Elimination ....................................................................... 120 3.5 Exercises for Chapter 3....................................................................... 126 4 Model Theory of Several Algebraic Theories......................................... 129 4.1 Ordered Abelian Groups..................................................................... 129 4.2 Ordered Fields.................................................................................... 136 4.3 Valued Fields: Examples and Properties.............................................140 ix
x Contents 4.4 4.5 4.6 4.7 Algebraically Closed Valued Fields ......................................................149 Real Closed Valued Fields......................................................................154 Henselian Fields ......................................................................................159 Exercises for Chapter 4............................................................................169 Appendix A: Remarks on Decidability................................................................171 Appendix B: Remarks on Second-Order Logic..................................................177 References..................................................................................................................185 Glossary of Notation................................................................................................187 Index..........................................................................................................................189
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| any_adam_object | 1 |
| author | Prestel, Alexander 1941-2024 Delzell, Charles N. 1953- |
| author_GND | (DE-588)117718777 (DE-588)173395597 |
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| author_role | aut aut |
| author_sort | Prestel, Alexander 1941-2024 |
| author_variant | a p ap c n d cn cnd |
| building | Verbundindex |
| bvnumber | BV039547220 |
| classification_rvk | SK 130 |
| ctrlnum | (OCoLC)754169437 (DE-599)BVBBV039547220 |
| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| isbn | 9781447121756 |
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| physical | X, 193 S. |
| publishDate | 2011 |
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| spelling | Prestel, Alexander 1941-2024 Verfasser (DE-588)117718777 aut Einführung in die Mathematische Logik und Modelltheorie Mathematical logic and model theory a brief introduction Alexander Prestel ; Charles N. Delzell London [u.a.] Springer 2011 X, 193 S. txt rdacontent n rdamedia nc rdacarrier Universitext Informatik Mathematik Computer science Mathematics Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Modelltheorie (DE-588)4114617-7 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Mathematische Logik (DE-588)4037951-6 s Modelltheorie (DE-588)4114617-7 s DE-604 Delzell, Charles N. 1953- Verfasser (DE-588)173395597 aut Erscheint auch als Online-Ausgabe 978-1-4471-2176-3 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024399169&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Prestel, Alexander 1941-2024 Delzell, Charles N. 1953- Mathematical logic and model theory a brief introduction Informatik Mathematik Computer science Mathematics Mathematische Logik (DE-588)4037951-6 gnd Modelltheorie (DE-588)4114617-7 gnd |
| subject_GND | (DE-588)4037951-6 (DE-588)4114617-7 (DE-588)4151278-9 |
| title | Mathematical logic and model theory a brief introduction |
| title_alt | Einführung in die Mathematische Logik und Modelltheorie |
| title_auth | Mathematical logic and model theory a brief introduction |
| title_exact_search | Mathematical logic and model theory a brief introduction |
| title_full | Mathematical logic and model theory a brief introduction Alexander Prestel ; Charles N. Delzell |
| title_fullStr | Mathematical logic and model theory a brief introduction Alexander Prestel ; Charles N. Delzell |
| title_full_unstemmed | Mathematical logic and model theory a brief introduction Alexander Prestel ; Charles N. Delzell |
| title_short | Mathematical logic and model theory |
| title_sort | mathematical logic and model theory a brief introduction |
| title_sub | a brief introduction |
| topic | Informatik Mathematik Computer science Mathematics Mathematische Logik (DE-588)4037951-6 gnd Modelltheorie (DE-588)4114617-7 gnd |
| topic_facet | Informatik Mathematik Computer science Mathematics Mathematische Logik Modelltheorie Einführung |
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