Answer by Farmer S for Precipitous ideal and inner model
No. Suppose otherwise. Let $G$ be the Levy collapse generic, and $D$ be the generic for forcing with the nonstationary ideal after that. Since $\mathrm{Ult}(L[U,G],D)$ is wellfounded, letting...
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Assume $\kappa$ is measurable, $U$ is its unique normal measure, $V=L[U]$. We levy collapse $\kappa$ to make it become $\omega_1$.If we don't have the inner model condition, then we only know that...
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