Title: Existentially closed models and locally zero-dimensional toposes Show Chinese title

Title: 存在闭模型和局部零维到范畴

Abstract: The notion of an existentially closed model is generalised to a property of geometric morphisms between toposes. We show that important properties of existentially closed models extend to existentially closed geometric morphisms, such as the fact that every model admits a homomorphism to an existentially closed one. Other properties do not generalise: classically, there are two equivalent definitions of an existentially closed model, but this equivalence breaks down for the generalised notion. We study the interaction of these two conditions on the topos-theoretic level, and characterise the classifying topos of the e.c. geometric morphisms when the conditions coincide. Show Chinese abstract

Abstract: 存在闭模型的概念被推广到到论之间几何态射的性质。 我们证明了存在闭模型的重要性质可以扩展到存在闭几何态射，例如每个模型都可到一个存在闭模型的同态。 其他性质则不具有普遍性：在经典情况下，存在闭模型有两种等价定义，但对于推广后的概念，这种等价性不成立。 我们研究了这两个条件在到论理论层面的相互作用，并在条件一致时刻画了存在闭几何态射的分类到论。