 Variables of \(L\) will be treated as variables of \(L^{\ast}\), forgetting about sorts. The difference between the many-sorted language \(L\) and the corresponding one-sorted one, \(L^{\ast}\), is that we add new unary relation symbols \(Q_{i}\), for each \(i\in \Sort\). Moreover, the symbols in \(\OperSym\) of \(L\) are also in \(L^{\ast}\) but while in the former language they have arity and sorts, in the latter they only have arity.