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arXiv · 1304.5438

Simple strategies for Banach-Mazur games and fairly correct systems

Thomas Brihaye·Quentin Menet
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Abstract

In 2006, Varacca and Völzer 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 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.

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Thomas Brihaye, Quentin Menet. 2013-07-17. Simple strategies for Banach-Mazur games and fairly correct systems. https://doi.org/10.4204/eptcs.119.5

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