## Journal of Symbolic Logic

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

Marion Scheepers

#### 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].

#### Article information

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

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183744501

Mathematical Reviews number (MathSciNet)
MR1276636

Zentralblatt MATH identifier
0805.54042

JSTOR
Scheepers, Marion. Meager Nowhere-Dense Games (IV): $n$-Tactics. J. Symbolic Logic 59 (1994), no. 2, 603--605. https://projecteuclid.org/euclid.jsl/1183744501