 if there is an isomorphism from one to the other. Now if Q is a generalized quantifier of type \({\langle}n_1,\ldots,n_k{\rangle}\), \(P_i\) is an \(n_i\)-ary predicate symbol for \(1\leq i\leq k\), \(\M = (M,I)\) is a model for the vocabulary \(\{P_1,\ldots,P_k\}\), and \(R_i = I(P_i)\), we also write