# 2020 seminar talk: Regularity properties in singular generalized descriptive set theory

Talk held by Vincenzo Dimonte (University of Udine, Italy) at the KGRC seminar on 2020-02-12.

### Abstract

Generalized descriptive set theory is the study of definable subsets of the space ${}^\kappa 2$ with the bounded topology. Such study has been overwhelmingly focussed on the case with $\kappa$ regular. Motivated by the theory of rank-into-rank cardinals, we concentrated instead on the case of $\kappa$ singular of cofinality $\omega$, painting a picture that is quite similar to the classical descriptive set theory case. This talk is going to center around the generalization of regularity properties (Perfect Set Property and Baire Property) in this context. The PSP is still akin to the classical case, while the BP probably needs more large-cardinal power to be non-trivial.