Classification and Orbit Equivalence Relations (Mathematical Surveys & Monographs) - Hardcover

Greg Hjorth

Hardcover

ISBN 10: 0821820028 ISBN 13: 9780821820025

Publisher: American Mathematical Society, 1999

Synopsis

Actions of Polish groups are ubiquitous in mathematics. In certain branches of ergodic theory and functional analysis, one finds a systematic study of the group of measure-preserving transformations and the unitary group. In logic, the analysis of countable models intertwines with results concerning the actions of the infinite symmetric group. This text develops the theory of Polish group actions entirely from scratch, ultimately presenting a coherent theory of the resulting orbit equivalence classes that may allow complete classification by invariants of an indicated form. The book concludes with a criterion for an orbit equivalence relation classifiable by countable structures considered up to isomorphism. This self-contained volume offers a complete treatment of this active area of current research and develops a difficult general theory classifying a class of mathematical objects up to some relevant notion of isomorphism or equivalence. Greg Hjorth received the Carol Karp Prize for outstanding work on turbulence and countable Borel equivalence relations from the Association of Symbolic Logic.

About this title

From the Publisher

This monograph is an important contribution to the ongoing study ... of definable equivalence relations on Polish spaces ... essential reading for anyone interested in the subject of definable equivalence relations, but is also important for mathematicians working in areas lying outside the usual boundaries of set theory.

Zentralblatt f\"ur Mathematik

Edition details

• Publisher: American Mathematical Society
• Publication date: 1999
• ISBN 10: 0821820028
• ISBN 13: 9780821820025
• Binding: Hardcover
• Language: English
• Edition number: 1
• Number of pages: 195