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

Abstract

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