Compact metrizable structures and classification problems

2016/10/02 by Rosendal, Christian, Zielinski, Joseph · 1 citation
#03E15 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1610.00370

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.

Cited by

• Applications of Borel-definable homological algebra to locally compact groups

Related

• The complexity of the homeomorphism relation between compact metric\n spaces
• Turbulence, orbit equivalence, and the classification of nuclear C*-algebras
• Isomorphism of almost locally compact Polish metric structures
• Completeness of the isomorphism problem for separable C*-algebras
• Classification and Non-classification of Homeomorphism Relations