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Covering Games and the Banach-Mazur Game: K-tactics

  • Tomek Bartoszynski (a1), Winfried Just (a1) and Marion Scheepers (a2)

Abstract

Given a free ideal J of subsets of a set X, we consider games where player ONE plays an increasing sequence of elements of the σ-completion of J, and player TWO tries to cover the union of this sequence by playing one set at a time from J. We describe various conditions under which player TWO has a winning strategy that uses only information about the most recent k moves of ONE, and apply some of these results to the Banach-Mazurgame.

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References

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C] Choquet, G., Lectures in Analysis, Vol. I, Benjamin, New York, 1969.
[Ci] Cichon, J., On two-cardinal properties of ideals, Transactions of the Amer. Math. Soc. 314(1989), 693-708.
[C-N] Comfort, W. W. and Negrepontis, S., Chain conditions in topology, Cambridge University Press, 1982.
[D] Debs, G., Straté;gies gagnantes dans certains jeux topologiques, Fundamenta Mathematicae 126(1985), 93-105.
[F-K] Fleissner, W. G. and Kunen, K., Barely Baire Spaces, Fundamenta Mathematicae 101(1978), 229-240.
[Fo] Foreman, M., personal communication, summer, 1992.
[F] Fremlin, D. H., Cichori's diagram. In: Séminaire d'Initiation à l'Analyse, Univ. Pierre et Marie Curie, Paris 23(1985), 5.01-5.13.
[G-T] Galvin, F. and Telgarsky, R., Stationary strategies in topological games, Topology and its Applications 22(1986), 51-69.
[I] Isbell, J. R., The category of cofinal types. II, Transactions of the A.M.S. 116(1965), 394-416.
[J] Jech, T., Multiple Forcing, Cambridge University Press, 1986.
[J-M-P-S] Just, W., Mathias, A. R. D., Prikry, K. and Simon, P., On the existence of large p-ideals, J. Symbolic Logic, (1990), 457-465.
[Ko] Koszmider, P., On Coherent Families of Finite-to-One Functions, J. Symbolic Logic, to appear.
[K] Kunen, K., Random and Cohen reals. In: Handbook of Set-Theoretic Topology, (eds. Kunen, K. and Vaughan, J. E.), Elsevier Science Publishers, 1984, 887-911.
[L] Laver, R., Linear orders in U(UJ) under eventual dominance, Logic Colloquium ‘78, North-Holland, (1979), 299-302.
[L-M-S] Levinski, J., Magidorand, M. Shelah, S., Chang's conjecture for 𝒩, Israel J. Math. 69(1990), 161-172.
[M] Miller, A. W., Some properties of measure and category, Trans. Amer. Math. Soc. 266(1981), 93-114.
[SI] Scheepers, M. Meager-nowheredense games (I): n-tactics, Rocky Mountain J. Math. 22(1992), 1011-1055.
[S2] Scheepers, M. A partition relation for partially ordered sets, Order 7(1990), 41-64.
[S3] Scheepers, M., Meager-nowhere dense games (IV): n-tactics and coding strategies, preprint.
[T] Telgarsky, R., Topological games: on the 50-th anniversary of the Banach-Mazur game, Rocky Mountain J. Math. 17(1987), 227-276.
[Toi] Todorcevic, S., Reals and Positive Partition Relations. In: Logic, Methodology and Philosophy of Science VII, (eds. Marcus, B. et al.), Elsevier Science Publishers, 1986, 159-169.
[To2] Todorcevic, S., Kurepa families and cofinal similarities, December, 1989, preprint.
[To3] Todorcevic, S., Cofinal Kurepa Families, November, 1990, preprint.
[To4] Todorcevic, S., Partitioning pairs of countable sets, Proceedings of the Amer. Math. Soc. 111(1991), 841-844.
[To5] Todorcevic, S., Partitioning pairs of countable ordinals, Acta Mathematica 159(1987), 261-294.
[W] Woodin, W. H., Discontinuous homomorphisms of C(Omega) and Set Theory, Ph.D. dissertation, University of California, Berkeley, 1984.
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Covering Games and the Banach-Mazur Game: K-tactics

  • Tomek Bartoszynski (a1), Winfried Just (a1) and Marion Scheepers (a2)

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