 Theorem 7 (Scott 1961) Suppose \(\kappa\) is a measurable cardinal. If \(\phi\) is a second-order sentence and \(\phi\) has a model \(\mm\) of cardinality \(\kappa\), then for every \(X\subseteq M\) of cardinality \(&lt;\kappa\) there is \(\mn\subseteq\mm\) such that \(X\subseteq N\), \(|N|\kappa\), and \(\mn\models\phi\).  [9] 