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The ideal determined by the unsymmetric game. (English) Zbl 0778.03016

Summary: We study the ideal of all subsets of \({\mathcal H}^ \omega\) for which the second player has a winning strategy in the unsymmetric game. We describe its cardinal coefficients and the notions of forcing determined by it.

MSC:

03E60 Determinacy principles
03E15 Descriptive set theory
03E40 Other aspects of forcing and Boolean-valued models
91A05 2-person games
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[1] James E. Baumgartner, Iterated forcing, Surveys in set theory, London Math. Soc. Lecture Note Ser., vol. 87, Cambridge Univ. Press, Cambridge, 1983, pp. 1 – 59. · Zbl 0524.03040
[2] Morton Davis, Infinite games of perfect information, Advances in game theory, Princeton Univ. Press, Princeton, N.J., 1964, pp. 85 – 101. · Zbl 0133.13104
[3] D. Fremlin, Cichon’s diagram, Seminaire Initiation a l’Analyse , 23e annee, 1983/84, no. 5.
[4] Thomas Jech, Set theory, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. Pure and Applied Mathematics. · Zbl 0419.03028
[5] A. S. Kechris, A. Louveau, and W. H. Woodin, The structure of \?-ideals of compact sets, Trans. Amer. Math. Soc. 301 (1987), no. 1, 263 – 288. · Zbl 0633.03043
[6] Jan Mycielski, On the axiom of determinateness. II, Fund. Math. 59 (1966), 203 – 212. · Zbl 0192.04204
[7] Andrzej Rosłanowski, On game ideals, Colloq. Math. 59 (1990), no. 2, 159 – 168. · Zbl 0724.04003
[8] Marek Balcerzak and Andrzej Rosłanowski, On Mycielski ideals, Proc. Amer. Math. Soc. 110 (1990), no. 1, 243 – 250. · Zbl 0708.04002
[9] Jan van Mill and George M. Reed , Open problems in topology, North-Holland Publishing Co., Amsterdam, 1990. · Zbl 0718.54001
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