Section: New Results

Descriptive Set Theory

• Participants: Mathieu Hoyrup

Descriptive Set Theory (DST) aims at classifying sets and functions in terms of the complexity of describing them. It is closely related to logic and computation theory, where sets and functions can be described by logical formulas or computer programs. DST was originally developed on a restricted class of topological spaces, the Polish spaces, which does not cover important classes of spaces that are needed in Theoretical Computer Science, especially in programming semantics, notably (Scott) domains or spaces of higher-order (Kleene-Kreisel) functionals. We investigate DST on such spaces and show that it does not work as nicely as on usual spaces. The article [29] is currently submitted. This work has been presented during an invited talk at CiE 2018 [13].