Strong ultrapowers and long core models

Abstract

In his paper [7] Steel asked whether there can exist a normal measure U on a cardinal κ such thatWe use Reverse Easton forcing to show that this is consistent from a P2κ hypermeasure; we also show that the result is sharp, using the core model for nonoverlapping coherent extender sequences.The proof uses forcing technology due to Woodin.In this section we collect some facts that are useful in the forcing constructions of the next section. None of them are due to us, and we are unsure to whom they should be attributed for the most part. We give sketchy proofs; the reader who wants to see more details is referred to [2].