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Actions of Polish Groups and Classification Problems

Kechris, Alexander S. (2003) Actions of Polish Groups and Classification Problems. In: Analysis and Logic. London Mathematical Society lecture note series. No.262. Cambridge University Press , Cambridge, pp. 115-187. ISBN 9780521648615. https://resolver.caltech.edu/CaltechAUTHORS:20130612-095807587

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Abstract

We will discuss in this paper some aspects of a general program whose goal is the development of the theory of definable actions of Polish groups, the structure and classification of their orbit spaces, and the closely related study of definable equivalence relations. This work is motivated by basic foundational questions, like understanding the nature of complete classification of mathematical objects up to some notion of equivalence by invariants, and creating a mathematical framework for measuring the complexity of such classification problems. This theory, which has been growing rapidly over the last few years, is developed within the context of descriptive set theory, which provides the basic underlying concepts and methods. On the other hand, in view of the broad scope of this theory, there are natural interactions of it with other areas of mathematics, such as the theory of topological groups, topological dynamics, ergodic theory and its relationships with the theory of operator algebras, model theory, and recursion theory.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://www.cambridge.org/us/knowledge/isbn/item1160418/Analysis%20and%20Logic/?site_locale=en_USPublisherUNSPECIFIED
Additional Information:© 2002 Cambridge University Press. Publication date: January 2003. Research and preparation of this paper have been partially supported by NSF Grants DMS 96-19880 and DMS 99-87437.
Funders:
Funding AgencyGrant Number
NSFDMS 96-19880
NSFDMS 99-87437
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Other Numbering System NameOther Numbering System ID
MathSciNet ReviewMR1967835
Series Name:London Mathematical Society lecture note series
Issue or Number:262
Record Number:CaltechAUTHORS:20130612-095807587
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20130612-095807587
Official Citation: Analysis and Logic C. Ward Henson, José Iovino, Alexander S. Kechris, Edward Odell, Catherine Finet, Christian Michaux Paperback (ISBN-13: 9780521648615) Publication date: March 2003 Subject: Logic categories and sets Series London Mathematical Society Lecture Note Series (No. 262)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38909
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:12 Jun 2013 20:18
Last Modified:03 Oct 2019 05:02

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