Notes on the equiconsistency of ZFC without the Power Set axiom and second order PA

Vladimir Kanovei, Vassily Lyubetsky

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 absenc…