论文标题
二阶理论的反思具有丰富的尿液元素双裂型枢机主教
Reflection in second-order set theory with abundant urelements bi-interprets a supercompact cardinal
论文作者
论文摘要
在回顾了尿元集理论中的各种自然双解释之后，包括二阶设置的理论，并在这些情况下探索了二阶反射的强度。最终，我们证明了具有丰富原子公理的二阶反射是双重的，因此与存在超级紧张的红衣主教的存在也相当。证明依赖于超级紧度的反思表征，即，当且仅当在结构$ m $（任何大小）中，在$ m \ prec m $ ys ys Bac $ m $ $ by $ m $ m $ m $ bec $κ上，每个$ m $（任何大小）中的每个$π^1_1 $句子都是超级compact thue of Bluce bes y Bate $κ$也是如此。
After reviewing various natural bi-interpretations in urelement set theory, including second-order set theories with urelements, we explore the strength of second-order reflection in these contexts. Ultimately, we prove, second-order reflection with the abundant atom axiom is bi-interpretable and hence also equiconsistent with the existence of a supercompact cardinal. The proof relies on a reflection characterization of supercompactness, namely, a cardinal $κ$ is supercompact if and only if every $Π^1_1$ sentence true in a structure $M$ (of any size) containing $κ$ in a language of size less than $κ$ is also true in a substructure $m\prec M$ of size less than $κ$ with $m\capκ\inκ$.
