**May 21**

**Omer Ben-Neria**,
Hebrew University

**Mathias-type Criterion for the Magidor Iteration of Prikry forcings**

In his seminal work on the identity crisis of strongly compact cardinals, Magidor introduced a special iteration of Prikry forcings for a set of measurable cardinals known as the Magidor iteration. The purpose of this talk is to present a Mathias-type criterion which characterizes when a sequence of omega-sequences is generic for the Magidor iteration. The result extends a theorem of Fuchs, who introduced a Mathias criterion for discrete products of Prikry forcings. We will present the new criterion, discuss several applications, and outline the main ideas of the proof.