Set-theoretic reflection is equivalent to induction over well-founded classes
Logic
2021-07-07 v3
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.
Cite
@article{arxiv.1909.00677,
title = {Set-theoretic reflection is equivalent to induction over well-founded classes},
author = {Anton Freund},
journal= {arXiv preprint arXiv:1909.00677},
year = {2021}
}