Strongly compact Magidor forcing
نویسنده
چکیده
We present a strongly compact version of the Supercompact Magidor forcing ([3]). A variation of it is used to show that the following is consistent: V ⊇ W are transitive models of ZFC+GCH with the same ordinals such that: 1. κ is an inaccessible in W , 2. κ changes its cofinality to ω1 in V witnessed by a club ⟨κα | α < ω1⟩, 3. for every α < ω1, (κ ++ α ) W < κα , 4. (κ++)W = κ+. 1 Preliminary settings. Assume GCH. Let κ be a κ−supercompact cardinal and j : V → M be a witnessing embedding. Denote the normal measure over κ derived from j by U , i.e.
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