${\Sigma}^0_3$ determinacy and ${\mathbf{\Pi}}^1_2$ monotone induction

Abstract

Building on recent work of Philip Welch, we prove that (lightface) $\Sigma^0_3$ determinacy is equivalent to the existence of a wellfounded model satisfying the axiom scheme of (boldface) $\mathbf{\Pi}^1_2$ monotone induction.