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- W744920664 abstract "In 2006, Varacca and Völzer proved that on finite graphs, ω-regular large sets coincide with ω-regular sets of probability 1, by using the existence of positional strategies in the related Banach–Mazur games. Motivated by this result, we try to understand relations between sets of probability 1 and various notions of simple strategies (including those introduced in a recent paper of Grädel and Leßenich). Then, we introduce a generalisation of the classical Banach–Mazur game and in particular, a probabilistic version whose goal is to characterise sets of probability 1 (as classical Banach–Mazur games characterise large sets). We obtain a determinacy result for these games, when the winning set is a countable intersection of open sets." @default.
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- W744920664 date "2015-12-01" @default.
- W744920664 modified "2023-10-14" @default.
- W744920664 title "Simple strategies for Banach–Mazur games and sets of probability 1" @default.
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- W744920664 doi "https://doi.org/10.1016/j.ic.2015.06.004" @default.
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