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

Marion Scheepers
Source: J. Symbolic Logic Volume 59, Issue 2 (1994), 603-605.

#### Abstract

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].

Primary Subjects: 03E99
Secondary Subjects: 04A99, 90D44
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