Katětov order and its applications

This talk is an overview of my recent articles on ideals on countable sets. I will present set-theoretic and topological applications of Katětov order on ideals, focusing on distinguishing certain classes of sequentially compact spaces and comparing certain classes of ultrafilters with the class of P-points. Moreover, I will discuss connections of Katětov order with descriptive properties of ideals, answering questions of M. Hrušák and of G. Debs and J. Saint Raymond. This talk is partially joint with R. Filipów, K. Kowitz and J. Tryba.