The descriptive set theory of Polish group actions:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Press
1996
|
| Edition: | 1. publ. |
| Series: | London Mathematical Society lecture note series
232 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 136 S. |
| ISBN: | 0521576059 |
Staff View
MARC
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| 245 | 1 | 0 | |a The descriptive set theory of Polish group actions |c Howard Becker ; Alexander S. Kechris |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
PREFACE vii
INTRODUCTION viii
0. DESCRIPTIVE SET THEORY 1
1. POLISH GROUPS 3
1.1 Metrizable groups 3
1.2 Polish groups 3
1.3 Examples 7
1.4 Universal Polish groups 7
1.5 Some facts about the symmetric group S^ 8
1.6 Standard Borel and Polishable groups 11
2. ACTIONS OF POLISH GROUPS 13
2.1 G spaces 13
2.2 Polish G spaces 14
2.3 Borel G spaces 17
2.4 Examples 20
2.5 The logic actions 22
2.6 Universal actions 22
2.7 Universal actions for closed subgroups of Soo 28
3. EQUIVALENCE RELATIONS 33
3.1 Generalities 33
3.2 Equivalence relations induced by actions 34
3.3 The Silver Dichotomy 34
3.4 The Glimm Effros Dichotomy 35
3.5 Universal equivalence relations 41
4. INVARIANT MEASURES
AND PARADOXICAL DECOMPOSITIONS 44
4.1 Tarski s Theorem 44
4.2 Countable decompositions 44
4.3 Nadkarni s Theorem 45
4.4 Proof of 4.2.1 46
4.5 Sketch of proof of Nadkarni s Theorem 47
4.6 Concluding remarks and problems 52
vi Contents
5. BETTER TOPOLOGIES 53
5.1 Finer topologies and Borel sets 53
5.2 Topological realization of Borel G spaces 58
5.3 Topological realization of definable G spaces 67
5.4 Finer topologies on G spaces 71
6. MODEL THEORY AND THE VAUGHT CONJECTURE 82
6.1 Background on the Vaught Conjecture 82
6.2 The Topological Vaught Conjecture 87
6.3 Atomic models 96
7. ACTIONS WITH BOREL
ORBIT EQUIVALENCE RELATIONS 98
7.1 Characterizations 98
7.2 Some effective considerations 103
7.3 Decompositions 104
7.4 Tame groups 108
7.5 Normalizers 110
8. DEFINABLE CARDINALITY 116
8.1 Orbit cardinality 116
8.2 Orbit cardinality for specific groups 119
References 122
Index 132
|
| any_adam_object | 1 |
| author | Becker, Howard Paul 1899-1960 Kechris, Alexander S. 1946- |
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| dewey-full | 514.32 |
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| dewey-ones | 514 - Topology |
| dewey-raw | 514.32 |
| dewey-search | 514.32 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| indexdate | 2024-07-09T18:04:26Z |
| institution | BVB |
| isbn | 0521576059 |
| language | English |
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| physical | XI, 136 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Cambridge Univ. Press |
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| series | London Mathematical Society lecture note series |
| series2 | London Mathematical Society lecture note series |
| spelling | Becker, Howard Paul 1899-1960 Verfasser (DE-588)118654500 aut The descriptive set theory of Polish group actions Howard Becker ; Alexander S. Kechris 1. publ. Cambridge Cambridge Univ. Press 1996 XI, 136 S. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society lecture note series 232 Polish spaces (Mathematics) Set theory Deskriptive Mengenlehre (DE-588)4149180-4 gnd rswk-swf Polnische Gruppe (DE-588)4438947-4 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf Gruppenoperation (DE-588)4158467-3 gnd rswk-swf Polnische Gruppe (DE-588)4438947-4 s DE-604 Deskriptive Mengenlehre (DE-588)4149180-4 s Gruppenoperation (DE-588)4158467-3 s Topologie (DE-588)4060425-1 s Kechris, Alexander S. 1946- Verfasser (DE-588)109300025 aut London Mathematical Society lecture note series 232 (DE-604)BV000000130 232 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007456916&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Becker, Howard Paul 1899-1960 Kechris, Alexander S. 1946- The descriptive set theory of Polish group actions London Mathematical Society lecture note series Polish spaces (Mathematics) Set theory Deskriptive Mengenlehre (DE-588)4149180-4 gnd Polnische Gruppe (DE-588)4438947-4 gnd Topologie (DE-588)4060425-1 gnd Gruppenoperation (DE-588)4158467-3 gnd |
| subject_GND | (DE-588)4149180-4 (DE-588)4438947-4 (DE-588)4060425-1 (DE-588)4158467-3 |
| title | The descriptive set theory of Polish group actions |
| title_auth | The descriptive set theory of Polish group actions |
| title_exact_search | The descriptive set theory of Polish group actions |
| title_full | The descriptive set theory of Polish group actions Howard Becker ; Alexander S. Kechris |
| title_fullStr | The descriptive set theory of Polish group actions Howard Becker ; Alexander S. Kechris |
| title_full_unstemmed | The descriptive set theory of Polish group actions Howard Becker ; Alexander S. Kechris |
| title_short | The descriptive set theory of Polish group actions |
| title_sort | the descriptive set theory of polish group actions |
| topic | Polish spaces (Mathematics) Set theory Deskriptive Mengenlehre (DE-588)4149180-4 gnd Polnische Gruppe (DE-588)4438947-4 gnd Topologie (DE-588)4060425-1 gnd Gruppenoperation (DE-588)4158467-3 gnd |
| topic_facet | Polish spaces (Mathematics) Set theory Deskriptive Mengenlehre Polnische Gruppe Topologie Gruppenoperation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007456916&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000130 |
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