The Descriptive Set Theory of Polish Group Actions

London Mathematical Society Lecture Note #232

by Howard S. 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. 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.

152 pages, Kindle Edition

First published December 5, 1996

About the author

Howard Saul Becker was an American sociologist who taught at Northwestern University.