Determinacy
subfield of set theory,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) property of a game whereby such a strategy exists
Determinacy is a subfield of game theory and set theory 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.
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.
Basic notions
Games
The first sort of game we shall consider is the two-player game of perfect information of length ω, in which the players play natural numbers. These games are often called Gale–Stewart games.
In this sort of game there are two players, often named I and II, who take turns playing natural numbers, with I going first. They play "forever"; that is, their plays are indexed by the natural numbers. When they're finished, a predetermined condition decides which player won.
“Determinacy” enters the record as subfield of set theory,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) property of a game whereby such a strategy exists. Crown Archives preserves that source wording while asking what Determinacy, subfield and theory can confirm, complicate or overturn.
Why this record matters
“Determinacy” is worth following because a concise public description often conceals a longer documentary argument. Here, Determinacy, subfield and theory provides the most credible route into that argument.
Biographical claims are most persuasive when dates, appointments and relationships can be traced to records created close to the events described. The source revision retrieved here is dated Jun 11, 2026. The linked authority identifier is Q1201165. None of the 0 selected statements returned an explicit reference. The first chronological checks are 1950.
Public reputation and documentary evidence do not always develop together; absence from a summary is not evidence of historical absence. The lead is largely declarative, so disagreement and counter-evidence require a deliberate search beyond the opening account. Authority statements aid reconciliation but still require their own references, qualifiers and ranks to be checked.
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This entry incorporates text from “Determinacy” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.