Subsystems of second order arithmetic:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin ; Heidelberg ; New York ; Barcelona ; Budapest
Springer
1999
|
| Series: | Perspectives in mathematical logic
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 444 S. |
| ISBN: | 3540648828 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Table of Contents
Preface VII
Acknowledgements IX
Table of Contents XI
I. Introduction 1
1.1 The Main Question 1
1.2 Subsystems of Z2 2
1.3 The System ACA0 6
1.4 Mathematics Within ACA0 9
1.5 77i CAo and Stronger Systems 15
1.6 Mathematics Within il^ CAo 18
1.7 The System RCA0 23
1.8 Mathematics Within RCA0 26
1.9 Reverse Mathematics 31
1.10 The System WKL0 35
1.11 The System ATR0 37
1.12 The Main Question, Revisited 41
1.13 Outline of Chapters II Through X 43
1.14 Conclusions 59
Part A. Development of Mathematics
Within Subsystems of Z2
II. Recursive Comprehension 63
11.1 The Formal System RCA0 63
11.2 Finite Sequences 65
11.3 Primitive Recursion 69
11.4 The Number Systems 73
11.5 Complete Separable Metric Spaces 78
11.6 Continuous Functions 84
11.7 More on Complete Separable Metric Spaces 88
XII Table of Contents
11.8 Mathematical Logic 91
11.9 Countable Fields 96
11.10 Separable Banach Spaces 99
11.11 Conclusions 103
III. Arithmetical Comprehension 105
111.1 The Formal System ACA0 105
111.2 Sequential Compactness 106
111.3 Strong Algebraic Closure 110
111.4 Countable Vector Spaces Ill
111.5 Maximal Ideals in Countable Commutative Rings 115
111.6 Countable Abelian Groups 117
111.7 Konig s Lemma and Ramsey s Theorem 121
111.8 Conclusions 125
IV. Weak Konig s Lemma 127
IV.l The Heine/Borel Covering Lemma 127
IV.2 Properties of Continuous Functions 132
IV.3 The Godel Completeness Theorem 139
IV.4 Formally Real Fields 141
IV.5 Uniqueness of Algebraic Closure 144
IV.6 Prime Ideals in Countable Commutative Rings 146
IV.7 Fixed Point Theorems 148
IV.8 Ordinary Differential Equations 153
IV.9 The Separable Hahn/Banach Theorem 160
IV.10 Conclusions 165
V. Arithmetical Transflnite Recursion 167
V.I Countable Well Orderings; Analytic Sets 167
V.2 The Formal System ATR0 173
V.3 Borel Sets 178
V.4 Perfect Sets; Pseudohierarchies 185
V.5 Reversals 189
V.6 Comparability of Countable Well Orderings 195
V.7 Countable Abelian Groups 199
V.8 S° and A°x Determinacy 203
V.9 The X? and A Ramsey Theorems 210
V.10 Conclusions 215
VI. n Comprehension 217
VI. 1 Perfect Kernels 217
VI.2 Coanalytic Uniformization 221
VI.3 Coanalytic Equivalence Relations 226
VI.4 Countable Abelian Groups 230
VI.5 Sf A 77? Determinacy 233
Table of Contents XIII
VI.6 The A Ramsey Theorem 236
VI.7 Stronger Set Existence Axioms 239
VI.8 Conclusions 241
Part B. Models of Subsystems of Z2
VII. /3 Models 245
VII. 1 The Minimum /3 Model of nj CAo 246
VII.2 Countable Coded ^ Models 250
VII.3 A Set Theoretic Interpretation of ATR0 260
VII.4 Constructible Sets and Absoluteness 275
VII.5 Strong Comprehension Schemes 289
VII.6 Strong Choice Schemes 296
VII.7 /3 Model Reflection 306
VII.8 Conclusions 310
VIII. w Models 313
VIII.l w Models of RCA0 and ACA0 314
VIII.2 Countable Coded w Models of WKL0 318
VIII.3 Hyperarithmetical Sets 326
VIII.4 w Models of E Choice 337
VIII.5 w Model Reflection and Incompleteness 347
VIII.6 w Models of Strong Systems 353
VIII.7 Conclusions 361
IX. Non w Models 363
IX.l The First Order Parts of RCA0 and ACA0 364
IX.2 The First Order Part of WKL0 369
IX.3 A Conservation Result for Hilbert s Program 373
IX.4 Saturated Models 383
IX.5 Gentzen Style Proof Theory 390
IX.6 Conclusions 392
Appendix
X. Additional Results 395
X.I Measure Theory 395
X.2 Separable Banach Spaces 401
X.3 Countable Combinatorics 403
X.4 Reverse Mathematics for RCA0 410
X.5 Conclusions 411
Bibliography 413
XIV Table of Contents
Index 425
List of Tables 445
|
| any_adam_object | 1 |
| author | Simpson, Stephen G. 1945- |
| author_GND | (DE-588)120428148 |
| author_facet | Simpson, Stephen G. 1945- |
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| author_sort | Simpson, Stephen G. 1945- |
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| 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 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV012196620 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:23:25Z |
| institution | BVB |
| isbn | 3540648828 |
| language | German |
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| physical | XIV, 444 S. |
| publishDate | 1999 |
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| publisher | Springer |
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| series2 | Perspectives in mathematical logic |
| spelling | Simpson, Stephen G. 1945- Verfasser (DE-588)120428148 aut Subsystems of second order arithmetic Stephen G. Simpson Berlin ; Heidelberg ; New York ; Barcelona ; Budapest Springer 1999 XIV, 444 S. txt rdacontent n rdamedia nc rdacarrier Perspectives in mathematical logic Calcul des prédicats Calcul des prédicats ram Logica gtt Modèles mathématiques ram Logik Predicate calculus Mathematik (DE-588)4037944-9 gnd rswk-swf Axiomatik (DE-588)4004038-0 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Grundlage (DE-588)4158388-7 gnd rswk-swf Mathematik (DE-588)4037944-9 s Grundlage (DE-588)4158388-7 s DE-604 Mathematische Logik (DE-588)4037951-6 s Axiomatik (DE-588)4004038-0 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008264454&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Simpson, Stephen G. 1945- Subsystems of second order arithmetic Calcul des prédicats Calcul des prédicats ram Logica gtt Modèles mathématiques ram Logik Predicate calculus Mathematik (DE-588)4037944-9 gnd Axiomatik (DE-588)4004038-0 gnd Mathematische Logik (DE-588)4037951-6 gnd Grundlage (DE-588)4158388-7 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4004038-0 (DE-588)4037951-6 (DE-588)4158388-7 |
| title | Subsystems of second order arithmetic |
| title_auth | Subsystems of second order arithmetic |
| title_exact_search | Subsystems of second order arithmetic |
| title_full | Subsystems of second order arithmetic Stephen G. Simpson |
| title_fullStr | Subsystems of second order arithmetic Stephen G. Simpson |
| title_full_unstemmed | Subsystems of second order arithmetic Stephen G. Simpson |
| title_short | Subsystems of second order arithmetic |
| title_sort | subsystems of second order arithmetic |
| topic | Calcul des prédicats Calcul des prédicats ram Logica gtt Modèles mathématiques ram Logik Predicate calculus Mathematik (DE-588)4037944-9 gnd Axiomatik (DE-588)4004038-0 gnd Mathematische Logik (DE-588)4037951-6 gnd Grundlage (DE-588)4158388-7 gnd |
| topic_facet | Calcul des prédicats Logica Modèles mathématiques Logik Predicate calculus Mathematik Axiomatik Mathematische Logik Grundlage |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008264454&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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