Simplicity theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Oxford Univ. Press
2014
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | Oxford logic guides
53 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 224 S. |
| ISBN: | 9780198567387 0198567383 |
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Datensatz im Suchindex
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| adam_text | Titel: Simplicity theory
Autor: Kim, Byunghan
Jahr: 2014
CONTENTS
1 Introduction........................................1
1.1 Model Theory 3
1.2 Stability 7
1.3 Bibliographical Remarks 11
2 Dividing, Forking, and Simplicity.........................12
2.1 Dividing and Forking 12
2.2 Simplicity and Forking 17
2.3 Dp,fc-Ranks and the Tree Property 21
2.4 Fundamental Theorem of Forking 29
2.5 Ranks and Supersimple Theories 31
2.6 Examples of Simple Theories 42
2.7 Bibliographical Remarks 44
3 Lascar Strong Types and Type Amalgamation.................45
3.1 Lascar Strong Types 45
3.2 Type Amalgamation 47
3.3 Characterizing Simple Theories 52
3.4 Bibliographical Remarks 54
4 Hyperimaginaries and Canonical Bases.....................SS
4.1 Hyperimaginaries 55
4.2 Non-forking Independence of Hyperimaginaries 60
4.3 Canonical Bases 66
4.4 Forking Relationships between Types 70
4.5 Bibliographical Remarks 80
5 Elimination of Hyperimaginaries.........................81
5.1 The Lascar Group 82
5.2 Lascar Types Are Strong Types in Low Theories 91
5.3 Elimination of Finitary Hyperimaginaries for Small Theories 92
5.4 Elimination of Hyperimaginaries for Supersimple Theories 96
5.5 Definability 101
5.6 Bibliographical Remarks 107
6 Constructing Simple Structures......................... 108
6.1 ModularityandCM-Triviality 109
6.2 Hrushovski Construction 113
X | CONTENTS
6.3 Generic Predicates/Automorphisms and Lovely Pairs 121
6.4 Bibliographical Remarks 125
7 Groups.........................................126
7.1 Type-Definable Groups 126
7.2 Hyperdefinable Groups 135
7.3 Commensurativity and Local Connectedness 141
7.4 1-Based Groups 147
7.5 Supersimple Groups 152
7.6 Generically Given Partial Groups and Homogeneous Spaces 163
7.7 Bibliographical Remarks 170
8 AGeometryof Forking...............................171
8.1 SU-Rank 1 Types 173
8.2 Non-affineLocallyModular Types 178
8.3 1-Based Types 182
8.4 Bibliographical Remarks 190
9 Generalized Amalgamation and the Group Configuration
Theorem........................................191
9.1 Generalized Amalgamation 192
9.2 The Group Configuration 198
9.3 The Generic Group Operation onF/R 204
9.4 An Application to 1-Based Theories 208
9.5 Recovering the Hyperdefinable Group Action 208
9.6 Bibliographical Remarks 215
References 217
Index 223
|
| adam_txt |
Titel: Simplicity theory
Autor: Kim, Byunghan
Jahr: 2014
CONTENTS
1 Introduction.1
1.1 Model Theory 3
1.2 Stability 7
1.3 Bibliographical Remarks 11
2 Dividing, Forking, and Simplicity.12
2.1 Dividing and Forking 12
2.2 Simplicity and Forking 17
2.3 Dp,fc-Ranks and the Tree Property 21
2.4 Fundamental Theorem of Forking 29
2.5 Ranks and Supersimple Theories 31
2.6 Examples of Simple Theories 42
2.7 Bibliographical Remarks 44
3 Lascar Strong Types and Type Amalgamation.45
3.1 Lascar Strong Types 45
3.2 Type Amalgamation 47
3.3 Characterizing Simple Theories 52
3.4 Bibliographical Remarks 54
4 Hyperimaginaries and Canonical Bases.SS
4.1 Hyperimaginaries 55
4.2 Non-forking Independence of Hyperimaginaries 60
4.3 Canonical Bases 66
4.4 Forking Relationships between Types 70
4.5 Bibliographical Remarks 80
5 Elimination of Hyperimaginaries.81
5.1 The Lascar Group 82
5.2 Lascar Types Are Strong Types in Low Theories 91
5.3 Elimination of Finitary Hyperimaginaries for Small Theories 92
5.4 Elimination of Hyperimaginaries for Supersimple Theories 96
5.5 Definability 101
5.6 Bibliographical Remarks 107
6 Constructing Simple Structures. 108
6.1 ModularityandCM-Triviality 109
6.2 Hrushovski Construction 113
X | CONTENTS
6.3 Generic Predicates/Automorphisms and Lovely Pairs 121
6.4 Bibliographical Remarks 125
7 Groups.126
7.1 Type-Definable Groups 126
7.2 Hyperdefinable Groups 135
7.3 Commensurativity and Local Connectedness 141
7.4 1-Based Groups 147
7.5 Supersimple Groups 152
7.6 Generically Given Partial Groups and Homogeneous Spaces 163
7.7 Bibliographical Remarks 170
8 AGeometryof Forking.171
8.1 SU-Rank 1 Types 173
8.2 Non-affineLocallyModular Types 178
8.3 1-Based Types 182
8.4 Bibliographical Remarks 190
9 Generalized Amalgamation and the Group Configuration
Theorem.191
9.1 Generalized Amalgamation 192
9.2 The Group Configuration 198
9.3 The Generic Group Operation onF/R 204
9.4 An Application to 1-Based Theories 208
9.5 Recovering the Hyperdefinable Group Action 208
9.6 Bibliographical Remarks 215
References 217
Index 223 |
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| discipline | Mathematik |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T22:02:36Z |
| indexdate | 2024-07-09T21:21:26Z |
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| isbn | 9780198567387 0198567383 |
| language | English |
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| spelling | Kim, Byunghan Verfasser (DE-588)1045089737 aut Simplicity theory Byunghan Kim 1. ed. Oxford Oxford Univ. Press 2014 X, 224 S. txt rdacontent n rdamedia nc rdacarrier Oxford logic guides 53 Model theory Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 s DE-604 Oxford logic guides 53 (DE-604)BV000013997 53 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016735213&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kim, Byunghan Simplicity theory Oxford logic guides Model theory Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4037951-6 |
| title | Simplicity theory |
| title_auth | Simplicity theory |
| title_exact_search | Simplicity theory |
| title_exact_search_txtP | Simplicity theory |
| title_full | Simplicity theory Byunghan Kim |
| title_fullStr | Simplicity theory Byunghan Kim |
| title_full_unstemmed | Simplicity theory Byunghan Kim |
| title_short | Simplicity theory |
| title_sort | simplicity theory |
| topic | Model theory Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Model theory Mathematische Logik |
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