Determinacy

Determinacy is a subfield of set theory, a branch of mathematics, that examines the conditions under which one or the other player of a game has a winning strategy, and the consequences of the existence of such strategies. Alternatively and similarly, "determinacy" is the property of a game whereby such a strategy exists. Determinacy was introduced by Gale and Stewart in 1950, under the name "determinateness".^[1]

The games studied in set theory are usually Gale–Stewart games—two-player games of perfect information in which the players make an infinite sequence of moves and there are no draws. The field of game theory studies more general kinds of games, including games with draws such as tic-tac-toe, chess, or infinite chess, or games with imperfect information such as poker.

^ Friedman, Harvey M. (2003). "Higher Set Theory and Mathematical Practice". In Sacks, Gerald E (ed.). Mathematical Logic in the 20th Century. co-published, World Scientific and Singapore University Press. pp. 49–81. doi:10.1142/9789812564894_0005. ISBN 978-981-02-4736-2.

[1] Friedman, Harvey M. (2003). "Higher Set Theory and Mathematical Practice". In Sacks, Gerald E (ed.). Mathematical Logic in the 20th Century. co-published, World Scientific and Singapore University Press. pp. 49–81. doi:10.1142/9789812564894_0005. ISBN 978-981-02-4736-2.

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