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

TL;DR

This paper establishes an equivalence between a specific form of game determinacy and a model-theoretic principle involving monotone induction at a certain descriptive set-theoretic level.

Contribution

It proves that lightface _3 determinacy is equivalent to the existence of a wellfounded model satisfying ^1_2 monotone induction, linking game theory and set theory.

Findings

_3 determinacy is equivalent to ^1_2 monotone induction in a wellfounded model.

The work extends the understanding of the relationship between determinacy and induction principles.

It builds on recent results by Philip Welch to establish this equivalence.

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.