 We wonder, can validity in the class of structures \(\mathfrak{S}^{\ast}\) be replaced by consequence from a set \(\Delta\) of many-sorted formulas? The next goal is to find such a \(\Delta\), at least a set satisfying \(\mathfrak{S}^{\ast}\subseteq \Mod(\Delta )\). To finish level one, one needs to prove a Representation theorem; namely, a statement of the following form: