Conversion of one-sorted structures into many-sorted ones Is any one-sorted structure \(\mathcal{E}\) of signature \(\Sigma ^{\ast}\) convertible into a many-sorted one of signature \(\Sigma\)? The answer is negative, as there are two problems that could stop the conversion: the first one is that in a many-sorted structure all the universes should be nonempty and our idea is to take for each sort \(i\) the unary relation \(Q_{i}^{\mathcal{E}}\) as universe of sort \(i\) and so we need it to be