 Notice that the structure \(\mathcal{A}^{\ast}\) of the previous theorem is a model of \(\Pi\). Moreover, a one-sorted model of \(\Pi\), \(\mathcal{E}\), is easily convertible into a many-sorted one, \(\mathcal{E}^{\ddag }\). We take \(Q_{i}^{\mathcal{E}}\) as the universe of sort \(i\), strict relations and functions are obtained as restrictions to the corresponding domains to obtain relations and functions with the desired  sorts.[29]  Due to the axioms in \(\Pi\), construction of \(\mathcal{E}^{\ddag }\) can be carried out. It is now easy to obtain the following result.