 From a many-sorted structure \(\mathcal{A}\) of signature \(\Sigma ^{\SOL}\) which is a model of \(\Delta\), we pass to another many-sorted structure \(\mathcal{B}\) of the same signature but where universes of sort \(\langle 1,\ldots ,1,0\rangle\) are now subsets of \(\wp (\mathbf{B}_{1}^{n})\) and \(\epsilon _{n}^{\mathcal{B}}\) is genuine membership. The new many-sorted structure \(\mathcal{B}\) is obtained by defining a function