 Every statement involving a generalized quantifier Q takes place within some universe M. Sometimes it is useful to be able to mirror this relativization to a universe inside M. This means defining a new quantifier with one extra set argument which says that Q behaves on the universe restricted to that argument exactly as it behaves on M. Thus, if Q is of type \({\langle}n_1,\ldots,n_k{\rangle}\), we define \(Q{^{\text{rel}}}\) of type \({\langle}1,n_1,\ldots,n_k{\rangle}\) as follows: