Elementary Submodels, Coding Strategies, and an Infinite Real Number Game - Clontz, Steven; Brian, Will (Topology Proceedings, 2023)
Matthew Baker [Math. Mag. 80 (2007), no. 5, pp. 377-380] investigates an elegant infinite-length game that may be used to study subsets of real numbers. We present two accessible examples of how an import ant technique from set theory or a different technique from infinite game theory may be used to answer Baker's question on whether this game provides a precise characterization for countable subsets of real numbers, and we connect this game to the well-studied Banach-Mazur game from topology.