The Magidor iteration and restrictions of ultrapowers to the ground model

Abstract We study the Magidor iteration of Prikry forcings below a measurable limit of measurables κ . We first characterize all the normal measures κ carries in the generic extension, building on and extending the main result of [1]. Then, for every such normal measure, we prove that the restriction of its ultrapower, from the generic extension to the ground model, is an iterated ultrapower of V by normal measures. This is done without core model theoretic assumptions; GCH ≤ κ in the ground model suffices.