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Set-theoretic reflection is equivalent to induction over well-founded classes
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-07-20 , DOI: 10.1090/proc/15103 Anton Freund
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-07-20 , DOI: 10.1090/proc/15103 Anton Freund
Abstract:We show that induction over 
-definable well-founded classes is equivalent to the reflection principle which asserts that any true formula of first order set theory with real parameters holds in some transitive set. The equivalence is proved in primitive recursive set theory (which is weaker than Kripke-Platek set theory) extended by the axiom of dependent choice.
中文翻译：
集合论的反思等同于对已有基础的课程的归纳
摘要：我们证明归纳超定义的良好基础类等同于反射原理，该原理主张具有某个实参的一阶集理论的任何真实公式都在某个传递集中成立。通过依赖选择公理扩展的原始递归集理论（比Kripke-Platek集理论弱）证明了等价性。
更新日期：2020-08-20
-definable well-founded classes is equivalent to the reflection principle which asserts that any true formula of first order set theory with real parameters holds in some transitive set. The equivalence is proved in primitive recursive set theory (which is weaker than Kripke-Platek set theory) extended by the axiom of dependent choice. 中文翻译：
集合论的反思等同于对已有基础的课程的归纳
摘要：我们证明归纳超定义的良好基础类等同于反射原理，该原理主张具有某个实参的一阶集理论的任何真实公式都在某个传递集中成立。通过依赖选择公理扩展的原始递归集理论（比Kripke-Platek集理论弱）证明了等价性。
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