标题： 关于ZFC不带幂集公理与二阶PA的等价一致性的注记 显示英文标题

标题： Notes on the equiconsistency of ZFC without the Power Set axiom and 2nd order PA

摘要： 我们证明了理论$\text{Z}^-$,$\text{ZF}^-$,$\text{ZFC}^-$（minus 表示 Power Set 公理的缺失）和$\text{PA}_2$,$\text{PA}_2^-$（minus 表示 Countable Choice 模式 的缺失）彼此等一致。 所使用的方法包括在$\text{PA}_2^-$中通过良好-founded 扩展性有向图解释无幂集的集合论，以及在所述无幂集集合论中的 Gödel 可构造性。 显示英文摘要

摘要： We demonstrate that theories $\text{Z}^-$, $\text{ZF}^-$, $\text{ZFC}^-$ (minus means the absence of the Power Set axiom) and $\text{PA}_2$, $\text{PA}_2^-$ (minus means the absence of the Countable Choice schema) are equiconsistent to each other. The methods used include the interpretation of a power-less set theory in $\text{PA}_2^-$ via well-founded extensional digraphs, as well as the G\"odel constructibility in the said power-less set theory.