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    Interpolation follows from metatheorems about the proof c... — Carmelics
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    Supports→Interpolation reveals a deep harmony between syntax and semantics in logic

    Interpolation follows from metatheorems about the proof calculus (proof-theoretic dimension)

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    Interpolation has significant model-theoretic applications including Beth's defi...Interpolation reveals a deep harmony between syntax and semantics in logicInterpolation thus lies at the intersection of proof theory and model theory

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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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