Journal of Symbolic Logic

Meager Nowhere-Dense Games (IV): $n$-Tactics

Marion Scheepers

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We consider the infinite game where player ONE chooses terms of a strictly increasing sequence of first category subsets of a space and TWO chooses nowhere dense sets. If after $\omega$ innings TWO's nowhere dense sets cover ONE's first category sets, then TWO wins. We prove a theorem which implies for the real line: If TWO has a winning strategy which depends on the most recent $n$ moves of ONE only, then TWO has a winning strategy depending on the most recent 3 moves of ONE (Corollary 3). Our results give some new information concerning Problem 1 of [S1] and clarifies some of the results in [B-J-S] and in [S1].

Article information

J. Symbolic Logic, Volume 59, Issue 2 (1994), 603-605.

First available in Project Euclid: 6 July 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 03E99: None of the above, but in this section
Secondary: 04A99 90D44


Scheepers, Marion. Meager Nowhere-Dense Games (IV): $n$-Tactics. J. Symbolic Logic 59 (1994), no. 2, 603--605.

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