The smooth ideal

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2016 Austria English Publisher:WileyJournal:Proceedings of the London Mathematical Society, volume 112, pages 57-80 (issn: 0024-6115, eissn: 1460-244X,

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Authors: Clemens, John; Conley, Clinton; Miller, Benjamin;

doi: 10.1112/plms/pdv069 , 10.1184/r1/6479987.v1 , 10.1184/r1/6479987

The smooth ideal

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Abstract

We give a classical proof of the generalization of the characterization of smoothness to quotients of Polish spaces by Borel equivalence relations. As an application, we describe the extent to which any given Borel equivalence relation on a Polish space is encoded by the corresponding σ-ideal generated by the family of Borel sets on which it is smooth.

Country

Austria

Related Organizations

University of Vienna
Austria
University of Illinois System
United States
Southern Illinois University Carbondale
United States
Carnegie Mellon University
United States

Keywords

SETS, equivalence relations, Other mathematical sciences not elsewhere classified, 101013 Mathematische Logik, smooth ideals, 101002 Analysis, Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets, smooth relations, 101013 Mathematical logic, \(E\)-smooth sets, Polish spaces, homogeneity of ideals, morphisms between ideals, Descriptive set theory, BOREL EQUIVALENCE-RELATIONS

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