Admissible sets and structures: an approach to definability theory
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1975
|
| Schriftenreihe: | Perspectives in mathematical logic
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 394 S. graph. Darst. |
| ISBN: | 3540074511 0387074511 |
Internformat
MARC
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| 245 | 1 | 0 | |a Admissible sets and structures |b an approach to definability theory |c Jon Barwise |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1975 | |
| 300 | |a XIII, 394 S. |b graph. Darst. | ||
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| 490 | 0 | |a Perspectives in mathematical logic | |
| 650 | 7 | |a Definieerbaarheid |2 gtt | |
| 650 | 4 | |a Définissabilité, Théorie de la (Logique mathématique) | |
| 650 | 4 | |a Ensembles admissibles | |
| 650 | 7 | |a Wiskundige logica |2 gtt | |
| 650 | 4 | |a Admissible sets | |
| 650 | 4 | |a Definability theory (Mathematical logic) | |
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Datensatz im Suchindex
| _version_ | 1804116406117072896 |
|---|---|
| adam_text | Table of Contents
Introduction 1
Part A. The Basic Theory 5
Chapter I. Admissible Set Theory 7
1. The Role of Urelements 7
2. The Axioms of KPU 9
3. Elementary Parts of Set Theory in KPU 11
4. Some Derivable Forms of Separation and Replacement 14
5. Adding Defined Symbols to KPU 18
6. Definition by £ Recursion 24
7. The Collapsing Lemma 30
8. Persistent and Absolute Predicates 33
9. Additional Axioms 38
Chapter II. Some Admissible Sets 42
1. The Definition of Admissible Set and Admissible Ordinal 42
2. Hereditarily Finite Sets 46
3. Sets of Hereditary Cardinality Less Than a Cardinal k 52
4. Inner Models: the Method of Interpretations 54
5. Constructible Sets with Urelements; IHYPs, Defined 57
6. Operations for Generating the Constructible Sets 62
7. First Order Definability and Substitutable Functions 69
8. The Truncation Lemma 72
9. The Levy Absoluteness Principle 76
Chapter III. Countable Fragments of LXi0 78
1. Formalizing Syntax and Semantics in KPU 78
2. Consistency Properties 84
3. 95J Logic and the Omitting Types Theorem 87
4. A Weak Completeness Theorem for Countable Fragments 92
5. Completeness and Compactness for Countable Admissible Fragments 95
XII Table of Contents
6. The Interpolation Theorem 103
7. Definable Well Ordenngs 105
8. Another Look at Consistency Properties 109
Chapter IV. Elementary Results on WYPj,, 113
1. On Set Existence 113
2. Defining Yl and 1} Predicates 116
3. Ilj and A{ on Countable Structures 122
4. Perfect Set Results 127
5. Recursively Saturated Structures 137
6. Countable SR Admissible Ordinals 144
7. Representability in 2Ji Logic 146
PartB. The Absolute Theory 151
Chapter V. The Recursion Theory of Z, Predicates on Admissible Sets . . 153
1. Satisfaction and Parametrization 153
2. The Second Recursion Theorem for KPU 156
3. Recursion Along Well founded Relations 158
4. Recursively Listed Admissible Sets 164
5. Notation Systems and Projections of Recursion Theory 168
6. Ordinal Recursion Theory: Projectible and Recursively Inaccessible
Ordinals 173
7. Ordinal Recursion Theory: Stability 177
8. Shoenfield s Absoluteness Lemma and the First Stable Ordinal . . 189
Chapter VI. Inductive Definitions 197
1. Inductive Definitions as Monotonic Operators 197
2. £ Inductive Definitions on Admissible Sets 205
3. First Order Positive Inductive Definitions and HYPm 211
4. Coding 1HFOT on M 220
5. Inductive Relations on Structures with Pairing 230
6. Recursive Open Games 242
Part C. Towards a General Theory 255
Chapter VII. More about Lxra 257
1. Some Definitions and Examples 257
2. A Weak Completeness Theorem for Arbitrary Fragments 262
3. Pinning Down Ordinals: the General Case 270
4. Indiscernibles and upward Lowenheim Skolem Theorems 276
5. Partially Isomorphic Structures 292
6. Scott Sentences and their Approximations 297
7. Scott Sentences and Admissible Sets 303
Table of Contents XIII
Chapter VIII. Strict n[ Predicates and Konig Principles 311
1. The Konig Infinity Lemma 311
2. Strict nj predicates: Preliminaries 315
3. Konig Principles on Countable Admissible Sets 321
4. Konig Principles K1 and K2 on Arbitrary Admissible Sets 326
5. Konig s Lemma and Nerode s Theorem: a Digression 334
6. Implicit Ordinals on Arbitrary Admissible Sets 339
7. Trees and X( Compact Sets of Cofinalityw 343
8. E, Compact Sets of Cofinality Greater than m 352
9. Weakly Compact Cardinals 356
Appendix. Nonstandard Compactness Arguments and the Admissible Cover. 365
1. Compactness Arguments over Standard Models of Set Theory . . . 365
2. The Admissible Cover and its Properties 366
3. An Interpretation of KPU in KP 372
4. Compactness Arguments over Nonstandard Models of Set Theory . 378
References 380
Index of Notation 386
Subject Index 388
|
| any_adam_object | 1 |
| author | Barwise, Jon 1942-2000 |
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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 |
| dewey-sort | 3511 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T15:38:00Z |
| institution | BVB |
| isbn | 3540074511 0387074511 |
| language | English |
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| physical | XIII, 394 S. graph. Darst. |
| publishDate | 1975 |
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| spelling | Barwise, Jon 1942-2000 Verfasser (DE-588)124163092 aut Admissible sets and structures an approach to definability theory Jon Barwise Berlin [u.a.] Springer 1975 XIII, 394 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Perspectives in mathematical logic Definieerbaarheid gtt Définissabilité, Théorie de la (Logique mathématique) Ensembles admissibles Wiskundige logica gtt Admissible sets Definability theory (Mathematical logic) Definierbarkeit (DE-588)4284514-2 gnd rswk-swf Mengenlehre (DE-588)4074715-3 gnd rswk-swf Axiomatik (DE-588)4004038-0 gnd rswk-swf Mengenlehre (DE-588)4074715-3 s Definierbarkeit (DE-588)4284514-2 s DE-604 Axiomatik (DE-588)4004038-0 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001280255&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 |
| spellingShingle | Barwise, Jon 1942-2000 Admissible sets and structures an approach to definability theory Definieerbaarheid gtt Définissabilité, Théorie de la (Logique mathématique) Ensembles admissibles Wiskundige logica gtt Admissible sets Definability theory (Mathematical logic) Definierbarkeit (DE-588)4284514-2 gnd Mengenlehre (DE-588)4074715-3 gnd Axiomatik (DE-588)4004038-0 gnd |
| subject_GND | (DE-588)4284514-2 (DE-588)4074715-3 (DE-588)4004038-0 |
| title | Admissible sets and structures an approach to definability theory |
| title_auth | Admissible sets and structures an approach to definability theory |
| title_exact_search | Admissible sets and structures an approach to definability theory |
| title_full | Admissible sets and structures an approach to definability theory Jon Barwise |
| title_fullStr | Admissible sets and structures an approach to definability theory Jon Barwise |
| title_full_unstemmed | Admissible sets and structures an approach to definability theory Jon Barwise |
| title_short | Admissible sets and structures |
| title_sort | admissible sets and structures an approach to definability theory |
| title_sub | an approach to definability theory |
| topic | Definieerbaarheid gtt Définissabilité, Théorie de la (Logique mathématique) Ensembles admissibles Wiskundige logica gtt Admissible sets Definability theory (Mathematical logic) Definierbarkeit (DE-588)4284514-2 gnd Mengenlehre (DE-588)4074715-3 gnd Axiomatik (DE-588)4004038-0 gnd |
| topic_facet | Definieerbaarheid Définissabilité, Théorie de la (Logique mathématique) Ensembles admissibles Wiskundige logica Admissible sets Definability theory (Mathematical logic) Definierbarkeit Mengenlehre Axiomatik |
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