Simple strategies for Banach-Mazur games and fairly correct systems

In 2006, Varacca and Voelzer proved that on finite graphs, omega-regular large sets coincide with omega-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 strategy (including those introduced in a recent paper of Graedel 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.

Authors

• Thomas Brihaye University of Mons
• Quentin Menet University of Mons

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