 There is another interesting idea, appearing explicitly in the 1953 paper, which is also useful. The idea is: If we weaken comprehension, we obtain a calculus between \(F^{\ast}\) and \(F^{\ast \ast}\). And it is easy to find a semantics for the logic thus defined. Of course, this class of structures is placed between \(\mathfrak{F}\) and \(\mathfrak{GS}\). The new logic, call it \(\XL\), will also be complete; the main reason being that this class of models is again axiomatizable.