Cardinal characteristics and singular cardinals

Abstract: Throughout the last few years, many generalizations from classical cardinal characteristics of the Baire space have been studied. Special interest has been given to the study of the combinatorics of the generalized Baire spaces $\kappa^\kappa$ when $\kappa$ is an uncountable regular cardinal (or even a large cardinal) but lately, the generalization to singular cardinals has also been the focus of interest. In this talk, I will present first the motivation within Set Theory to study these kinds of questions and afterward some results regarding a generalization to the context of singular cardinals of the concepts of maximal almost disjoint and maximal independence families and point out the differences concerning the regular case. Finally, I will mention the open questions and possible future research paths in this area.

logic

Audience: researchers in the topic

Online logic seminar

Series comments: Description: Seminar on all areas of logic