# Asaf Karagila: Restrictions on forcings that change cofinalities

Friday Set Theory Seminar (HUJI)

We shall meet this Friday (June 26th) in the Hebrew University math department building in Room 110, at 10 am.

Speaker: Asaf Karagila (HUJI)

Title: Restrictions on forcings that change cofinalities

Abstract: Given a regular cardinal kappa, we want to know what sort of “nice” properties a forcing can have while making kappa singular. For target cofinality omega we have the Prikry forcing which is homogeneous and does not add bounded subsets to kappa. But if we want the cofinality to be uncountable we run into problems. For example, sigma-closed forcings cannot change cofinalities without collapsing cardinals.

We will investigate a couple of nice properties a forcing might have, weaken them, and show that under reasonable conditions a forcing with these conditions cannot change the cofinality of a cardinal to be uncountable without collapsing it. Joint work with Yair Hayut.

See you there!