 We need only make minimal adjustments in the model theory in order to accommodate the expanded vocabulary of the classical theory of quantification and identity. A model \(\langle D, I \rangle\) will still consist of a non-empty domain, \(D\), and an interpretation function, \(I\). One difference, however, is that we now take \(I\), in addition, to assign a member of the domain \(D\) to each individual constant and to assign an \(n\)-place function from the set of ordered \(n\)-tuples of members of \(D\), \(D^{n}\), into \(D\) to each function symbol \(f^{n}_{i}\).