Borel determinacy gives a game-theoretic meaning to Borel sets and is invoked, e.g., to describe the Wadge hierarchy; finite-memory determinacy of Muller games and positional determinacy of parity games both connect logic and automata theory. All these various determinacy results involve two-player games with two possible outcomes saying who wins. First, I will show that all such determinacy results can be generalised for many outcomes instead of two; second, I will show that Borel determinacy can also be generalised for many players and many outcomes instead of two; third, I will mention a possible further generalisation of Borel determinacy that is not proved yet; and finally I will explain how a new result on finite tree-games might be generalised on the Baire space.

The three abstracts below give slightly more details:

[http://arxiv.org/abs/1203.1866v3 arxiv.org/abs/1203.1866v3]

[http://www.lmcs-online.org/ojs/viewarticle.php?id=985&layout=abstract&iid=39 www.lmcs-online.org/ojs/viewarticle.php]

[http://arxiv.org/abs/1309.2798 arxiv.org/abs/1309.2798]