论文标题
关于二元性和模型理论的多个空间
On duality and model theory for polyadic spaces
论文作者
论文摘要
本文是从二元性和分类逻辑的角度研究一阶相干逻辑的研究。我们证明了相干性高核和开放的多核priestley空间之间的双重定理，随后我们将其应用于证明完整性，省略类型和Craig interpolation定理，以进行连贯或直觉的逻辑。我们的方法强调了插值和开放性能的作用，并允许对这些模型理论结果进行模块化，无语法处理。作为相同方法的进一步应用，我们证明了恒定域和Gödel-Dummett直觉谓词逻辑的完整定理。
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.
