DETERMINACY AND MONOTONE INDUCTIVE DEFINITIONS

We prove the equivalence of the determinacy of Sigma(0)(3) (effectively G(delta sigma)) games with the existence of a beta-model satisfying the axiom of Pi(1/2) monotone induction, answering a question of Montalban [8]. The proof is tripartite, consisting of (i) a direct and natural proof of Sigma(0)(3) determinacy using monotone inductive operators, including an isolation of the minimal complexity of winning strategies; (ii) an analysis of the convergence of such operators in levels of Godel's L, culminating in the result that the nonstandard models isolated by Welch [18] satisfy Pi(1/2) monotone induction; and (iii) a recasting of Welch's [17] Friedman-style game to show that this determinacy yields the existence of one of Welch's nonstandard models. Our analysis in (iii) furnishes a description of the degree of Pi(1/)2 -correctness of the minimal beta-model of Pi(1/2) monotone induction.