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    The translation from many-sorted to one-sorted logic pres... — Carmelics
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    Supports→Compactness, Enumerability, and Löwenheim-Skolem theorems hold for many-sorted logic

    The translation from many-sorted to one-sorted logic preserves semantic consequence

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    We formalize the argument as: \[\begin{align} \alpha & :=\forall x(Ix\land \exists y(Oy\land Eyx)\rightarrow \forall z(Iz\land Pzx\rightarrow \exists v(Ov\land Evz))) \label{primerorden} \\ \beta & :=\exists y(Oy\land Eyt)\\ \gamma &:=\forall y(Iy\rightarrow Pdy)\\ \delta & :=\exists x(Ox\land Exd) \end{align} \] In order to derive the conclusion, we will need as well an extra hypothesis saying that the dawn of times and today are both times, \((Id\land It)\). We could add

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