 How does one establish facts about expressive power? It seems as if in order to show \(L_1 \leq L_2\) one has to go through all of the infinitely many sentences in \(L_1\) and for each one find an equivalent in \(L_2\). But in practice it suffices to show that the generalized quantifiers in \(L_1\) are definable in \(L_2\). If Q is of type \({\langle}1,2{\rangle}\), say, Q is definable in \(L_2\) if there is an \(L_2\)-sentence \(\p\) whose non-logical vocabulary consists exactly of one unary and one binary predicate symbol, such that for all models \(\M = (M,A,R)\),