论文标题
公理的高级集理论方法
An axiomatic approach to higher order set theory
论文作者
论文摘要
一段时间以来，高级集合理论一直是一个兴趣的话题，最近的努力集中在二阶设定理论的强度上[KW16]。在本文中，我们努力提出一种“集合理论”，以正式考虑“可计数高阶集理论”。我们将看到，该理论与$ ZFC $相当，加上不可访问的红衣主教的存在。我们还将看到，该理论是标准集/类理论（例如$ ZFC $或$ MK $）（例如类别理论）的数学某些部分的规范基础。
Higher order set theory has been a topic of interest for some time, with recent efforts focused on the strength of second order set theories [KW16]. In this paper we strive to present one 'theory of collections' that allows for a formal consideration of 'countable higher order set theory'. We will see that this theory is equiconsistent with $ZFC$ plus the existence of a countable collection of inaccessible cardinals. We will also see that this theory serves as a canonical foundation for some parts of mathematics not covered by standard set/class theories (e.g. $ZFC$ or $MK$), such as category theory.
