Meager-nowhere dense games (III): Remainder strategies

Marion Scheepers

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Meager-nowhere dense games (III): Remainder strategies

Marion Scheepers

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Abstract

Player ONE chooses a meager set and player TWO, a nowhere dense set per inning. They play $ω$ many innings. ONE's consecutive choices must form a (weakly) increasing sequence. TWO wins if the union of the chosen nowhere dense sets covers the union of the chosen meager sets. A strategy for TWO which depends on knowing only the uncovered part of the most recently chosen meager set is said to be a remainder strategy. Theorem (among others): TWO has a winning remainder strategy for this game played on the real line with its usual topology.

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Marion Scheepers. 1992-09-25. Meager-nowhere dense games (III): Remainder strategies. https://arxiv.org/abs/math/9209208

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