 The structures we want to work with are \(\MSL^{\SOL}\) models of extensionality and comprehension with disjoint universes. So, they have to be models of \(\Delta\). In such a model the universes of sort \(\langle 1,\ldots ,1,0\rangle\) are not necessarily subsets of \(\wp (\mathbf{A}_{1}^{n}).\) However, \(\mathbf{A}_{1}\) and \(\mathbf{A}_{\langle 1,\ldots ,1,0\rangle }\) are related by \(\epsilon _{n}^{\mathcal{A}}\), but this relation doesn’t need to be “genuine” membership.