Newelski, L.; Rosłanowski, A. The ideal determined by the unsymmetric game. (English) Zbl 0778.03016 Proc. Am. Math. Soc. 117, No. 3, 823-831 (1993). 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. Cited in 4 ReviewsCited in 12 Documents MSC: 03E60 Determinacy principles 03E15 Descriptive set theory 03E40 Other aspects of forcing and Boolean-valued models 91A05 2-person games Keywords:winning strategy; unsymmetric game; cardinal coefficients; forcing PDFBibTeX XMLCite \textit{L. Newelski} and \textit{A. Rosłanowski}, Proc. Am. Math. Soc. 117, No. 3, 823--831 (1993; Zbl 0778.03016) Full Text: DOI References: [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.