 A second-order general structure \(\mathcal{A}=\langle \mathbf{A},\langle \mathbf{A}_{n}\rangle _{n\in \mathbb{N}},\ldots \rangle\) could also be seen as many-sorted. As in standard structures, \(\mathcal{A}\) contains the domain of individuals \(\mathbf{A}\) as well as domains of n-ary relations for each natural number, \(\mathbf{A}_{n}\subseteq \wp (\mathbf{A}^{n})\). But since \(\mathcal{A}\) is a general structure, the universes \(\mathbf{A}_{n}\) are not arbitrarily chosen, for the reason that they must satisfy the Comprehension Schema. Therefore, the universes are closed under definability (more information on general structures in  section 4.1).