= Nested transitive models from a worldly cardinal
A <worldly cardinal> permits a <countable transitive model> $M$ of <ZFC> and a <transitive model> $N$ of <ZFC> with $M\in N$, $|N|=\aleph_1$, and $(\omega_1)^N=\omega_1$. First collapse a countable <elementary substructure> of $V_\kappa$. Then collapse an $\aleph_1$-sized <Skolem hull> containing every countable ordinal and every member of $M$, as well as $M$ itself. The <transitive collapse fixes transitive subsets> lemma preserves $M$ and those ordinals.
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