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Infinite games. Combinatorial game theory for infinite two-player games of perfect information. Open games, clopen games. Determinacy. Transfinite game values. Topological games.

21 votes

Checkmate in $\omega$ moves?

Dropping the assumption of finitely many pieces as in this answer, we construct for any countable ordinal $\alpha$ a position having mate in $\beta > \alpha$, so $\gamma = \omega_1$ in the context of …
Matthew Bolan's user avatar