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Countable Borel Equivalence Relations
| Venue: | J. MATH. LOGIC |
| Citations: | 87 - 12 self |
BibTeX
@ARTICLE{Jackson_countableborel,
author = {S. Jackson and A. S. Kechris and A. Louveau},
title = {Countable Borel Equivalence Relations},
journal = {J. MATH. LOGIC},
year = {},
volume = {2},
pages = {1--80}
}
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Abstract
This paper is a contribution to a new direction in descriptive set theory that is being extensively pursued over the last decade or so. It deals with 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 study 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. (For an extensive discussion of these matters, see, e.g., Hjorth [00], Kechris [99, 00a].) This theory is developed within the context of descriptive set theory, which provides the basic underlying concepts and methods. On the other hand, in view of its broad scope, there are natural interactions of it with other areas of mathematics, such as model theory, recursion theory, the theory of topological groups and their representations, topological dynamics, ergodic theory, and operator algebras
Keyphrases
countable borel equivalence relation descriptive set theory broad scope topological dynamic recursion theory extensive discussion last decade ergodic theory polish group model theory orbit space classification problem natural interaction basic underlying concept operator algebra basic foundational question definable action mathematical framework new direction mathematical object definable equivalence relation related study complete classification topological group
