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COMPACT METRIZABLE STRUCTURES AND CLASSIFICATION PROBLEMS

Published online by Cambridge University Press:  01 May 2018

CHRISTIAN ROSENDAL  and
JOSEPH ZIELINSKI
CHRISTIAN ROSENDAL
Affiliation:
DEPARTMENT OF MATHEMATICS, STATISTICS, AND COMPUTER SCIENCE (M/C 249) UNIVERSITY OF ILLINOIS AT CHICAGO 851 S. MORGAN ST. CHICAGO, IL 60607-7045, USA E-mail: rosendal.math@gmail.com URL: http://homepages.math.uic.edu/∼rosendal
JOSEPH ZIELINSKI
Affiliation:
DEPARTMENT OF MATHEMATICAL SCIENCES CARNEGIE MELLON UNIVERSITY WEAN HALL 6113 PITTSBURGH, PA 15213, USA E-mail: zielinski.math@gmail.com URL: http://math.cmu.edu/∼zielinski/
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Abstract

We introduce and study the framework of compact metric structures and their associated notions of isomorphisms such as homeomorphic and bi-Lipschitz isomorphism. This is subsequently applied to model various classification problems in analysis such as isomorphism of C*-algebras and affine homeomorphism of Choquet simplices, where among other things we provide a simple proof of the completeness of the isomorphism relation of separable, simple, nuclear C*-algebras recently established by M. Sabok.

Keywords

03E15Borel reducibilitycompact metrizable structurescomplexity of classification problems

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Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 1 , March 2018 , pp. 165 - 186
Copyright
Copyright © The Association for Symbolic Logic 2018 

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References

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