Prelegent: Piotr Borodulin-Nadzieja

We show a way to handle names for ultrafilters in the random forcing.
Using this approach we reprove Kunen's theorem about long towers in the random model and Kamburelis' characterization of Boolean algebras supporting finitely additive measures.
The talk represents joint works with Damian Sobota and Katarzyna Cegielka.