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We address definability questions in propositional intuitionistic logic via an embedding of the opposite of the category of finitely presented Heyting algebras into a suitable sheaf topos. The closure properties of such an embedding are established by combinatorial arguments relying on Ehrenfeucht-Fraissé games. Applications are given to model-completability, fixpoints definability, projectivity, and unification theory.

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Investigating Definability in Propositional Logic via Sheaves on Grothendieck Topologies

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  • 发表日期：

    2025年

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  • Silvio Ghilardi

摘要

We address definability questions in propositional intuitionistic logic via an embedding of the opposite of the category of finitely presented Heyting algebras into a suitable sheaf topos. The closure properties of such an embedding are established by combinatorial arguments relying on Ehrenfeucht-Fraissé games. Applications are given to model-completability, fixpoints definability, projectivity, and unification theory.