COMPACT METRIZABLE STRUCTURES AND CLASSIFICATION PROBLEMS.

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 <italic>C</italic>*-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 <italic>C</italic>*-algebras recently established by M. Sabok. [ABSTRACT FROM AUTHOR]