Original Articles


Published in: Quaestiones Mathematicae
Volume 17, issue 4, 1994 , pages: 419–435
DOI: 10.1080/16073606.1994.9631775
Author(s): Marion ScheepersDepartment of Mathematics,
Keywords: 90D44


Players ONE and TWO play the following game of length ω: In the n-th inning ONE first chooses a meager subset of the real line; TWO responds with a nowhere dense set. TWO wins only if the union of TWO'S nowhere dense sets is exactly equal to the union of ONE'S first category sets. We prove that TWO has a winning strategy, even if TWO remembers only the most recent two moves each inning (Corollary 8). We show that in a closely related game, the assertion that TWO has a winning strategy depending on only the most recent two moves each inning is equivalent to a weak version of the Singular Cardinals Hypothesis (Theorem 1).

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