Abstract We consider of constructing normal ultrafilters in extensions are here Easton support iterations of Prikry-type forcing notions. New ways presented. It turns out that, in contrast with other supports, seemingly unrelated measures or extenders can be involved here.

We continue the study started in [2] and characterize j ↾ V , where j : V [ G ] → M [ H ] is an ultrapower embedding by a normal ultrafilter after a non-stationary support iteration of Prikry forcings.

Let P be a forcing notion and $G\subseteq P$ its generic subset. Suppose that we have in $V[G]$ a $\kappa{-}$ complete ultrafilter1,2W over $\kappa $ . Set $U=W\cap V$ .