The Descriptive Set Theory of Polish Group Actions

ISBN-13: 9780521576055 / Angielski / Miękka / 1996 / 152 str.

Howard Becker; Alexander S. Kechris; J. W. S. Cassels

Opis

A Polish space (group) is a separable, completely metrizable topological space (group). This book is about actions of Polish groups, in connection with--or from the point of view of--the subject of descriptive set theory. Descriptive set theory is the study of definable sets and functions in Polish spaces. The basic classes of definable sets are the classes of Borel, analytic and coanalytic sets, and these constitute the main topic of the book, but the authors also consider other classes of definable sets. This will be a valuable book for all researchers in set theory and related areas.

Recenzje

"This is an excellent book for anyone interested in Borel sets and analytic sets...in separable spaces whose topologies can be given by complete metrics...." Arlan Ramsay, Journal of Symbolic Logic

Spis treści

Descriptive set theory; 1. Polish groups; 2. Actions of polish groups; 3. Equivalence relations; 4. Invariant measures and paradoxical decompositions; 5. Better topologies; 6. Model theory and the Vaught conjecture; 7. Actions with Borel orbit equivalence relations; 8. Definable cardinality; References.