This is a talk for the New York Set Theory Seminar on March 1, 2013.
This talk will be based on my recent paper with C. D. A. Evans, Transfinite game values in infinite chess.
Infinite chess is chess played on an infinite chessboard. Since checkmate, when it occurs, does so after finitely many moves, this is technically what is known as an open game, and is therefore subject to the theory of open games, including the theory of ordinal game values. In this talk, I will give a general introduction to the theory of ordinal game values for ordinal games, before diving into several examples illustrating high transfinite game values in infinite chess. The supremum of these values is the omega one of chess, denoted by