A Canonical Model for Presheaf Semantics

Abstract : Presheaf models [Osius, 1975, Fourman and Scott, 1979, Moerdijk and Mac Lane, 1992] are a simple generalization of Kripke models and provide one of the most natural semantics for intuitionistic predicate logic. Although a completeness result for this semantics is known, this is usually obtained either non-constructively, by defi ning a canonical Kripke model,or indirectly, e.g. via categorical equivalences with omega-models as in [Troelstra and Van Dalen, 1988]. This paper describes an elementary canonicalmodel construction by means of which completeness is established in a perspicuous, direct and constructive way.
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https://hal.inria.fr/inria-00618862
Contributor : Ivano Alessandro Ciardelli <>
Submitted on : Saturday, September 3, 2011 - 5:35:47 PM
Last modification on : Thursday, January 11, 2018 - 6:20:16 AM
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Ivano Ciardelli. A Canonical Model for Presheaf Semantics. Topology, Algebra and Categories in Logic (TACL) 2011, Jul 2011, Marseille, France. ⟨inria-00618862⟩

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