The Magidor Iteration and Restrictions of Ultrapowers to the Ground Model

Eyal Kaplan

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arXiv · 2202.04980

The Magidor Iteration and Restrictions of Ultrapowers to the Ground Model

Eyal Kaplan

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Abstract

We study the Magidor iteration of Prikry forcings below a measurable limit of measurables $ \kappa $. We first characterize all the normal measures $ \kappa $ carries in the generic extension, building on and extending the main result of \cite{ben2014forcing}. 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; $ \mbox{GCH}_{\leq \kappa} $ in the ground model suffices.

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BibTeX RIS

Eyal Kaplan. 2022-02-10. The Magidor Iteration and Restrictions of Ultrapowers to the Ground Model. https://arxiv.org/abs/2202.04980

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