 The domain of \(\mathcal{A}^{\ast}\) is the union of the individuals domains of \(\mathcal{A}\), the interpretation of the new unary predicates \(Q_{i}\) corresponds to the old domains \(\mathbf{A}_{i}\) and so this information is kept. The interpretation of the rest of elements in \(\OperSym\) is similar to the one they have in the many-sorted structure \(\mathcal{A}\). The only difficulty concerns operation symbols with \(\Rank(f)=\langle i_{1},\ldots ,i_{n},i_{0}\rangle\) and \(i_{0}\not=0\) because now the universe is the union of the universes and function \(f^{\mathcal{A}^{\ast}}\) needs to give values to all of then. It is worth noting that for every \(f^{\mathcal{A}}\) there are many different operations extending it, which means that there are different one-sorted structures generated by the above  conversion.[28]