Set theory seminarFriday, September 18, 201510:00 amGC 3212

# Boolean ultrapowers and the Bukovsky-Dehornoy phenomenon

## Gunter Fuchs

### The City University of New York

I will present a criterion for when an ultrafilter on a Boolean algebra gives rise to the Bukovsky-Dehornoy phenomenon, namely that the intersection of all intermediate ultrapowers is equal to the the Boolean model. Time permitting, I will show that the Boolean algebras of Prikry and Magidor forcing satisfy the strong Prikry property, and that these forcings come with a canonical imitation iteration whose limit model is the Boolean ultrapower by a very canonical ultrafilter on their respective Boolean algebras.

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

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on September 11th, 2015