# Magidor Forcing

## Gunter Fuchs

### The City University of New York

In this talk, I am going to present a forcing designed by Magidor in the late seventies to change the cofinality of a measurable cardinal without collapsing cardinals. Previously, Prikry had introduced a forcing that changes the cofinality of a measurable cardinal to $omega$. Magidor’s forcing has more flexibility, but needs stronger assumptions also, and it is quite complex. After giving some background and showing the basic properties of Magidor forcing, I will prove a combinatorial characterization of genericity of sequences added by the forcing. There are some similarities to the situation of Prikry forcing, where an $omega$-sequence of ordinals less than the measurable cardinal is generic iff it is almost contained in any measure one set, as was shown by Mathias. I will show or sketch a proof of the corresponding characterization in the case of Magidor forcing in the second part of the talk next week.

Gunter Fuchs is a professor at The City University of New York, and conducts research in mathematical logic and especially set theory.