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- W2950271034 abstract "We propose a new, game-theoretic, approach to the idealized forcing, in terms of fusion games. This generalizes the classical approach to the Sacks and the Miller forcing. For definable ($mathbf{Pi}^1_1$ on $mathbf{Sigma}^1_1) $sigma$-ideals we show that if a $sigma$-ideal is generated by closed sets, then it is generated by closed sets in all forcing extensions. We also prove an infinite-dimensional version of the Solecki dichotomy for analytic sets. Among examples, we investigate the $sigma$-ideal $E$ generated by closed null sets and $sigma$-ideals connected with not piecewise continuous functions." @default.
- W2950271034 created "2019-06-27" @default.
- W2950271034 creator A5040694509 @default.
- W2950271034 date "2009-10-13" @default.
- W2950271034 modified "2023-09-23" @default.
- W2950271034 title "Forcing, games and families of closed sets" @default.
- W2950271034 hasPublicationYear "2009" @default.
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