标题： 无限阶一阶范畴逻辑 显示英文标题

标题： Infinitary first-order categorical logic

摘要： 我们提供了一种统一的范畴论处理方法，用于几种经典和直觉主义无穷逻辑的完备性定理，并提出了一个公理化方案。 这提供了新的完备性定理，并通过哥德尔、克里普克、贝斯、卡普、乔亚尔、马卡伊和福尔曼/格雷森的先前结果进行了概括。 作为应用，我们使用大基数假设证明了无穷直觉主义一阶逻辑的析取性和存在性性质。 显示英文摘要

摘要： We present a unified categorical treatment of completeness theorems for several classical and intuitionistic infinitary logics with a proposed axiomatization. This provides new completeness theorems and subsumes previous ones by G\"odel, Kripke, Beth, Karp, Joyal, Makkai and Fourman/Grayson. As an application we prove, using large cardinals assumptions, the disjunction and existence properties for infinitary intuitionistic first-order logics.