 The vocabulary of the classical theory of quantification and identity extends the vocabulary of pure quantificational logic with a set of individual constants with or without subscripts, \(a, b, c, a_1\), …, and a set of function symbols of various kinds: one-place function symbols, \(f^{1}, g^{1}, f^{1}_{1}\), …, two-place function symbols, \(f^{2}, g^{2}, g^{2}_{1}\),  etc.[5]  In addition to this, we may add a special two-place predicate, \(=\), for identity.