论文标题
分类大型红衣主教以及分类和固定理论反射之间的张力
Categorical large cardinals and the tension between categoricity and set-theoretic reflection
论文作者
论文摘要
受Zermelo的准算术结果的启发，表征了二阶Zermelo-fraenkel设置理论$ \ text {zfc} _2 $的模型，我们研究了这些模型完全分类的何时，以$ \ text {zfc} _2 _2 _2 _2 _2 _2 $的第一阶句子，一阶理论，第二订单理论，第二阶 - 第二订单，第二阶 - 第二阶句。因此，我们对分类大型红衣主教进行分析。这种数学分析自然而然地导致了有关结构主义和现实主义的哲学问题，尤其是分类和反思之间的张力。最终，我们确定了偏爱非类别基础的理由。
Inspired by Zermelo's quasi-categoricity result characterizing the models of second-order Zermelo-Fraenkel set theory $\text{ZFC}_2$, we investigate when those models are fully categorical, characterized by the addition to $\text{ZFC}_2$ either of a first-order sentence, a first-order theory, a second-order sentence or a second-order theory. Thus we mount an analysis of the categorical large cardinals. This mathematical analysis leads naturally to philosophical issues concerning structuralism and realism, including especially the tension between categoricity and reflection. Ultimately we identify grounds for the preference of noncategoricity in one's foundations.
