The descriptive set theory of Polish group actions [EBook] / Howard Becker, Alexander S. Kechris.
The descriptive set theory of Polish group actions [EBook] / Howard Becker, Alexander S. Kechris.
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. Nonlocally compact Polish groups occur naturally as g...
Personal Name(s):  Becker, Howard, (author) 

Kechris, A. S., (author)  
Imprint: 
Cambridge :
Cambridge University Press,
1996

Physical Description: 
1 online resource (136 pages) 
Note: 
englisch 
ISBN: 
9780521576055 9780511735264 
Series Title: 
London Mathematical Society lecture note series ;
232 
Subject (LOC):  
Full Text 
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. Nonlocally 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, GlimmEffros type dichotomies and the topological Vaught conjecture); descriptive complexity of orbit equivalence relations; definable cardinality of orbit spaces. 