论文标题
正式的模型理论和更高的拓扑
Formal Model Theory & Higher Topology
论文作者
论文摘要
我们研究了（广义）有界离子的$ 2 $类别BION和带有指示colimits的可访问类别的$ \ text {acc}_Ω$，作为接近正式模型理论的抽象框架。我们将它们与Topoi和（Lex）几何草图联系起来，这些草图是几何理论的分类规格。我们提供重建和类似完整的结果。我们将抽象基础类与本地可决定的托普伊联系起来。我们介绍了饱和对象的类别的概念，并将其与原子拓扑相关联。
We study the $2$-categories BIon, of (generalized) bounded ionads, and $\text{Acc}_ω$, of accessible categories with directed colimits, as an abstract framework to approach formal model theory. We relate them to topoi and (lex) geometric sketches, which serve as categorical specifications of geometric theories. We provide reconstruction and completeness-like results. We relate abstract elementary classes to locally decidable topoi. We introduce the notion of categories of saturated objects and relate it to atomic topoi.
