Kreisel-Lévy-type theorems for Kripke-Platek and other set theories

Shuangshuang Shu, Michael Rathjen

We prove that, over Kripke-Platek set theory with infinity (KP), transfinite induction along the ordinal ${\epsilon }_{\Omega +1}$ is equivalent to the schema asserting the soundness of KP, where…