Algebra Seminar talk
Combinatorics of ultrafilters on Boolean algebras
I will discuss some recent results about the structure of ultrafilters on Boolean algebras in the framework of Tukey reducibility. The main motivation is to understand and classify (not necessarily generic) ultrafilters on the algebras adjoining Cohen and random reals. Furthermore, I will highlight the connection with a cardinal invariant of Boolean algebras, the ultrafilter number, and sketch consistency results concerning its possible values.
This is joint work with Jörg Brendle, available at https://doi.org/10.1017/jsl.2021.18