 In this definition, model \(\mathcal{M}^{\prime }\) is considered an X-expansion of \(\mathcal{M}\) iff it includes as many new universes (\(\mathbf{M}_{i_{1}}^{\prime },\ldots ,\mathbf{M}_{i_{r}}^{\prime }\)) as the sorts of \(X\) requires. Moreover, the restriction of \(\mathcal{M}^{\prime }\) to the old ones is \(\mathcal{M}\).