A game for Baire's grand theorem

TL;DR

This paper introduces a game-theoretic characterization of Baire class 1 functions on separable metrizable spaces, linking game determinacy to a generalized Baire's grand theorem under various set-theoretic assumptions.

Contribution

It provides a new game that characterizes Baire class 1 functions and establishes the equivalence between game determinacy and a generalized Baire's grand theorem.

Findings

Game characterizes Baire class 1 functions.

Determinacy of the game is equivalent to the generalized Baire's grand theorem.

Results hold under AD and in Solovay's model.

Abstract

Generalizing a result of Kiss, we provide a game that characterizes Baire class 1 functions between arbitrary separable metrizable spaces. We show that the determinacy of our game is equivalent to a generalization of Baire's grand theorem, and that both these statements hold under AD and in Solovay's model.