Compact Structures in Descriptive Classification Theory

Generalized Descriptive Set Theory and Classification Theory

The field of descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper we study the generalization where countable is replaced by uncountable. We explore properties of generalized Baire and Cantor spaces, equivalence relations and their Borel reducibility. The study shows that the descriptive set theory looks very different in...

Descriptive Classification Theory and Separable Banach Spaces

Three Notions of Classification Consider your favorite class ofmathematical structures, be it groups, modules, measure-preserving transformations, C-algebras, Lie groups, smooth manifolds, or something completely different. With some probability, the classification problem for these objects, that is, the problem of determining the structures up to some relevant notion of isomorphism, is, or has...

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 C∗-algebras and affine homeomorphism of Choquet simplices, where among other things we provide a simple proof of the completeness ...

Descriptive Set Theory Descriptive Set Theory

Towards a descriptive set theory for domain-like structures

This is a survey of results in descriptive set theory for domains and similar spaces, with the emphasis on the ω-algebraic domains. We try to demonstrate that the subject is interesting in its own right and is closely related to some areas of theoretical computer science. Since the subject is still in its beginning, we discuss in detail several open questions and possible future development. We...