Borel equivalence relations
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Borel equivalence relations structure and classification by V. G. Kanoveĭ

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Published by American Mathematical Society in Providence, R.I .
Written in English


  • Equivalence relations (Set theory),
  • Equivalence classes (Set theory),
  • Borel sets

Book details:

Edition Notes

Includes bibliographical references and index.

StatementVladimir Kanovei.
SeriesUniversity lecture series -- v. 44
LC ClassificationsQA248 .K355 2008
The Physical Object
Paginationp. cm.
ID Numbers
Open LibraryOL16365812M
ISBN 109780821844533
LC Control Number2007060598

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Over the last 20 years, the theory of Borel equivalence relations and related topics have been very active areas of research in set theory and have important interactions with other fields of mathematics, like ergodic theory and topological dynamics, group theory, combinatorics, functional analysis, and model theory. a text book on the theory of Borel equivalence relations. 1 De nitions Before moving onto the theory of Borel equivalence relations it would be helpful to discuss Borel sets in general. A thorough and more complete account can be found in [46]. De nition A Polish space is a separable topological space which admits a compatible complete metric. Borel equivalence relations and cardinal algebras Alexander S. Kechris and Henry L. Macdonald 1 Introduction (A)In the late ’s Tarski published the book Cardinal Algebras, see [T], in which he developed an algebraic approach to the theory of cardinal addition, devoid of the use of the full Axiom of Choice, which of course trivializes it. Borel equivalence relations and cardinal algebras 3. (v) The results in (i){(iv) also hold for arbitrary Borel equivalence re- lations and . B replaced by vi B (as de ned after ). (B) This paper is organized as follows. In Section 2, we review the theory of cardinal algebras.

Section 2 we introduce countable Borel equivalence relations, discuss some of their properties and mention several examples. The scope of the theory of countable Borel equivalence relations is actually much wider as it encom-passes a great variety of other equivalence relations up to Borel bireducibility. Abstract. We show that every basis for the countable Borel equivalence relations strictly above $\mathbb{E}_0$ under measure reducibility is uncountable, thereby ruling out natural generalizations of the Glimm-Effros by: 3. In mathematics, a Borel equivalence relation on a Polish space X is an equivalence relation on X that is a Borel subset of X × X (in the product topology). Formal definition [ edit ] Given Borel equivalence relations E and F on Polish spaces X and Y respectively, one says that E is Borel reducible to F, in symbols E ≤ B F, if and only if there is a Borel function. Sets, Relations, Functions This note covers the following topics: Introduction to sets, Subsets, power sets, equality of sets, Finite and infinite sets, Set operations, De Morgan rules, distributivity, tables, Ordered pairs, Cartesian products, Introduction to relations, Ordering relations, Equivalence relations and .

The theory of Borel equivalence relations studies the set-theoretic nature of possible invariants and develops a mathematical framework for measuring the complexity of such classification Greg Hjorth. Dec 10,  · Borel Equivalence Relations. Abstract. This article surveys the rapidly evolving area of Borel equivalence relations under the ordering of Borel reducibility. Although the field is now considered part of descriptive set theory, it traces its origins back to areas entirely outside by: Jul 04,  · The study of Borel equivalence relations under Borel reducibility has developed into an important area of descriptive set theory. The dichotomies of . The space of Lascar strong types, on some sort and relative to a given first order theory T, is in general not a compact Hausdorff space. This paper has at.