Intersection Games and Bernstein Sets

Published 1 Oct 2023 in math.LO | (2310.03039v2)

Abstract: The Banach-Mazur game, Schmidt's game and McMullen's absolute winning game are three quintessential intersection games. We investigate their determinacy on the real line when the target set for either player is a Bernstein set, a non-Lebesgue measurable set whose construction depends on the axiom of choice.

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