Playing in the first Baire class



We present a self-contained analysis of some reduction games, which characterise various natural subclasses of the first Baire class of functions ranging from and into 0-dimensional Polish spaces. We prove that these games are determined, without using Martin's Borel determinacy, and give precise descriptions of the winning strategies for Player I. As an application of this analysis, we get a new proof of the Baire's lemma on pointwise convergence.