Skip to Main content Skip to Navigation
New interface
Preprints, Working Papers, ...

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.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

https://hal-cnrs.archives-ouvertes.fr/hal-03815128
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

Links full text

Identifiers

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

Collections

Citation

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

Share

Metrics

Record views

0