On duality and model theory for polyadic spaces

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2023-11-07 DOI:10.1016/j.apal.2023.103388

Sam van Gool, Jérémie Marquès

引用次数: 1

Abstract

This paper is a study of first-order coherent logic from the point of view of duality and categorical logic. We prove a duality theorem between coherent hyperdoctrines and open polyadic Priestley spaces, which we subsequently apply to prove completeness, omitting types, and Craig interpolation theorems for coherent or intuitionistic logic. 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 Gödel-Dummett intuitionistic predicate logics.

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多进空间的对偶性与模型理论

本文从对偶逻辑和范畴逻辑的角度研究一阶连贯逻辑。我们证明了相干超学说与开放多进Priestley空间之间的对偶定理，并应用该对偶定理证明了相干逻辑或直觉逻辑的完备性、省略类型和克雷格插值定理。我们的方法强调插值和开放属性的作用，并允许对这些模型理论结果进行模块化、无语法的处理。作为该方法的进一步应用，我们证明了常数域和Gödel-Dummett直觉谓词逻辑的完备性定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Pure and Applied Logic 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

200 days

期刊介绍： The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.