 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.