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On duality and model theory for polyadic spaces

Abstract : This paper is a study of first-order coherent logic from the point of view of duality and categorical logic. We start by characterizing the Priestley duals of coherent hyperdoctrines, the algebraization we take for coherent logic, as the open polyadic Priestley spaces. We then prove completeness, omitting types, and Craig interpolation theorems from this order-topological point of view. Our approach emphasizes the role of interpolation and openness properties, and allows for a modular, syntax-free treatment of these model-theoretic results. As further applications of the same method, we prove completeness theorems for constant domain and G\"odel-Dummett intuitionistic predicate logics.
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Preprints, Working Papers, ...
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Contributor : Sam van Gool Connect in order to contact the contributor
Submitted on : Friday, October 14, 2022 - 1:56:45 PM
Last modification on : Saturday, October 15, 2022 - 4:53:56 AM

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  • HAL Id : hal-03815128, version 1
  • ARXIV : 2210.01018



Sam van Gool, Jérémie Marquès. On duality and model theory for polyadic spaces. {date}. ⟨hal-03815128⟩



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