Boolean ultrapowers and the Bukovsky-Dehornoy phenomenon
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.