| Description |
1 online resource (136 pages) |
| Series |
London Mathematical Society lecture note series ; 232 |
|
London Mathematical Society lecture note series ; 232.
|
| Contents |
3.4 The Glimm-Effros Dichotomy3.5 Universal equivalence relations; 4. INVARIANT MEASURES AND PARADOXICAL DECOMPOSITIONS; 4.1 Tarski's Theorem; 4.2 Countable decompositions; 4.3 Nadkarni's Theorem; 4.4 Proof of 4.2.1; 4.5 Sketch of proof of Nadkarni's Theorem; 4.6 Concluding remarks and problems; 5. BETTER TOPOLOGIES; 5.1 Finer topologies and Borel sets; 5.2 Topological realization of Borel G-spaces; 5.3 Topological realization of definable G-spaces; 5.4 Finer topologies on G-spaces; 6. MODEL THEORY AND THE VAUGHT CONJECTURE; 6.1 Background on the Vaught Conjecture |
|
6.2 The Topological Vaught Conjecture6.3 Atomic models; 7. ACTIONS WITH BOREL ORBIT EQUIVALENCE RELATIONS; 7.1 Characterizations; 7.2 Some effective considerations; 7.3 Decompositions; 7.4 Tame groups; 7.5 Normalizers; 8. DEFINABLE CARDINALITY; 8.1 Orbit cardinality; 8.2 Orbit cardinality for specific groups; References; Index |
| Summary |
In this book the authors present their research into the foundations of the theory of Polish groups and the associated orbit equivalence relations. The particular case of locally compact groups has long been studied in many areas of mathematics. Non-locally compact Polish groups occur naturally as groups of symmetries in such areas as logic (especially model theory), ergodic theory, group representations, and operator algebras. Some of the topics covered here are: topological realizations of Borel measurable actions; universal actions; applications to invariant measures; actions of the infinite symmetric group in connection with model theory (logic actions); dichotomies for orbit spaces (including Silver, Glimm-Effros type dichotomies and the topological Vaught conjecture); descriptive complexity of orbit equivalence relations; definable cardinality of orbit spaces |
| Bibliography |
Includes bibliographical references (pages 122-131) and index |
| Notes |
Print version record |
| Subject |
Polish spaces (Mathematics)
|
|
Set theory.
|
|
MATHEMATICS -- Topology.
|
|
Polish spaces (Mathematics)
|
|
Set theory
|
|
Verzamelingen (wiskunde)
|
|
Lokaal compacte groepen.
|
|
Espaces polonais.
|
|
Ensembles, Théorie des.
|
| Form |
Electronic book
|
| Author |
Kechris, A. S., 1946-
|
| ISBN |
9781107362468 |
|
1107362466 |
|
