determinacy
Sign in to saveDeterminacy 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.
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Article
28 sectionsContents
- Basic notions
- Games
- Strategies
- Winning strategies
- Determined games
- Determinacy from elementary considerations
- Determinacy from [[ZFC]]
- Determinacy and large cardinals
- Measurable cardinals
- Proof of determinacy from sharps
- Woodin cardinals
- Projective determinacy
- Axiom of determinacy
- Consequences of determinacy
- Regularity properties for sets of reals
- Periodicity theorems
- Applications to decidability of certain second-order theories
- Wadge determinacy
- More general games
- Games in which the objects played are not natural numbers
- Games played on [[Tree (descriptive set theory)|trees]]
- Long games
- Games of imperfect information
- Quasistrategies and quasideterminacy
- See also
- Footnotes
- References
- External links
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.