Models of Peano arithmetic:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Clarendon Press
1991
|
| Schriftenreihe: | Oxford logic guides
15 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 292 S. |
| ISBN: | 019853213X |
Internformat
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Datensatz im Suchindex
| _version_ | 1804118666126557184 |
|---|---|
| adam_text | Contents
0. Background 1
0.1 Background model theory 2
0.2 Background recursion theory 5
1. The standard model 10
2. Discretely ordered rings 16
2.1 The axioms of PA~ 16
2.2 Initial segments and end extensions 21
3. Godel incompleteness 28
3.1 Xj formulas and the computable sets 28
3.2 Incompleteness 35
4. The axioms of Peano arithmetic 42
4.1 Alternative induction schemes 43
4.2 Introducing new relations and functions 47
5. Some number theory in PA 53
5.1 Euclidean division and Bezout s theorem 53
5.2 Godel s lemma 58
5.3 The infinitude of primes 65
6. Models of PA 69
6.1 Overspill 70
6.2 The order type of a model of PA 73
7. Collection 78
7.1 The arithmetic hierarchy 78
7.2 Cofinal extensions 86
8. Prime models 91
8.1 Definable elements 91
8.2 End extensions 96
ix
x Contents
9. Satisfaction 104
9.1 Sequences 105
9.2 Syntax 108
9.3 Semantics 119
10. Subsystems of PA 130
10.1 Indefinable elements 130
10.2 2n elementary initial segments 134
11 Saturation 141
11.1 Coded sets 141
11.2 2,, recursive saturation 146
11.3 Tennenbaum s theorem 153
12. Initial segments 159
12.1 Friedman s theorem 160
12.2 Variations 166
13. The standard system 172
13.1 Scott sets 172
13.2 The arithmetized completeness theorem 186
14. Indicators 193
14.1 What are indicators? 193
14.2 Recursively axiomatized theories have indicators 198
14.3 The Paris Harrington theorem 206
15. Recursive saturation 223
15.1 Satisfaction classes 224
15.2 Resplendency 247
16. Suggestions for further reading 266
Bibliography 276
Index 285
|
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| discipline | Informatik Mathematik |
| format | Book |
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| institution | BVB |
| isbn | 019853213X |
| language | English |
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| series | Oxford logic guides |
| series2 | Oxford logic guides |
| spelling | Kaye, Richard Verfasser aut Models of Peano arithmetic Richard Kaye Oxford Clarendon Press 1991 X, 292 S. txt rdacontent n rdamedia nc rdacarrier Oxford logic guides 15 Peano-Arithmetik (DE-588)4290970-3 gnd rswk-swf Arithmetik (DE-588)4002919-0 gnd rswk-swf Algebraische Modelltheorie (DE-588)4141842-6 gnd rswk-swf Peano-Axiomensystem (DE-588)4287500-6 gnd rswk-swf Modelltheorie (DE-588)4114617-7 gnd rswk-swf Arithmetik (DE-588)4002919-0 s Modelltheorie (DE-588)4114617-7 s DE-604 Peano-Axiomensystem (DE-588)4287500-6 s Algebraische Modelltheorie (DE-588)4141842-6 s Peano-Arithmetik (DE-588)4290970-3 s Oxford logic guides 15 (DE-604)BV000013997 15 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002789598&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kaye, Richard Models of Peano arithmetic Oxford logic guides Peano-Arithmetik (DE-588)4290970-3 gnd Arithmetik (DE-588)4002919-0 gnd Algebraische Modelltheorie (DE-588)4141842-6 gnd Peano-Axiomensystem (DE-588)4287500-6 gnd Modelltheorie (DE-588)4114617-7 gnd |
| subject_GND | (DE-588)4290970-3 (DE-588)4002919-0 (DE-588)4141842-6 (DE-588)4287500-6 (DE-588)4114617-7 |
| title | Models of Peano arithmetic |
| title_auth | Models of Peano arithmetic |
| title_exact_search | Models of Peano arithmetic |
| title_full | Models of Peano arithmetic Richard Kaye |
| title_fullStr | Models of Peano arithmetic Richard Kaye |
| title_full_unstemmed | Models of Peano arithmetic Richard Kaye |
| title_short | Models of Peano arithmetic |
| title_sort | models of peano arithmetic |
| topic | Peano-Arithmetik (DE-588)4290970-3 gnd Arithmetik (DE-588)4002919-0 gnd Algebraische Modelltheorie (DE-588)4141842-6 gnd Peano-Axiomensystem (DE-588)4287500-6 gnd Modelltheorie (DE-588)4114617-7 gnd |
| topic_facet | Peano-Arithmetik Arithmetik Algebraische Modelltheorie Peano-Axiomensystem Modelltheorie |
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