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Meager nowhere-dense games (IV): n-tactics (continued)

Published online by Cambridge University Press:  12 March 2014

Marion Scheepers
Marion Scheepers*
Affiliation:
Department of Mathematics, Boise State University, Boise, Idaho 83725, E-mail: marion@math.idbsu.edu
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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 ω 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].

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 59 , Issue 2 , June 1994 , pp. 603 - 605
Copyright
Copyright © Association for Symbolic Logic 1994

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References

REFERENCES

[B-J-S] Bartoszynski, T., Just, W., and Scheepers, M., Covering games and the Banach-Mazur game: k-tactics, The Canadian Journal of Mathematics, vol. 45 (1993), pp. 897–929.CrossRefGoogle Scholar
[J] Jech, T., Set Theory, Academic Press, New York, 1978.Google Scholar
[S1] Scheepers, M., Meager nowhere-dense games (I): n-tactics, The Rocky Mountain Journal of Mathematics, vol. 22 (1992), pp. 1011–1055.CrossRefGoogle Scholar
[S2] Scheepers, M., A partition relation for partially ordered sets, Order, vol. 7 (1990), pp. 41–64.CrossRefGoogle Scholar
[S3] Scheepers, M., Meager nowhere-dense games (II): coding strategies, Proceedings of the American Mathematical Society, vol. 112 (1991), pp. 1107–1115.Google Scholar
[S4] Scheepers, M., Meager nowhere-dense games (III): remainder strategies, Topology Proceedings (to appear).Google Scholar