In set theory, a branch of mathematics, **determinacy** is the study of under what circumstances one or the other player of a game must have a winning strategy, and the consequences of the existence of such strategies.

Read more about Determinacy: Determinacy From Elementary Considerations, Determinacy From ZFC, Determinacy and Large Cardinals, Quasistrategies and Quasideterminacy

### Other articles related to "determinacy":

Determinator -

... If there are infinitely many Woodin cardinals, then projective

**Determinacy**and Large Cardinals - Projective**Determinacy**... If there are infinitely many Woodin cardinals, then projective

**determinacy**holds that is, every game whose winning condition is a projective set is determined ... From projective**determinacy**it follows that, for every natural number n, there is a transitive inner model which satisfies that there are n Woodin cardinals ...Axioms Of Set Theory - Areas of Study -

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**Determinacy**...

**Determinacy**refers to the fact that, under appropriate assumptions, certain two-player games of perfect information are determined from the start in the sense that one player must have a winning ... The axiom of**determinacy**(AD) is an important object of study although incompatible with the axiom of choice, AD implies that all subsets of the ...Borel

... Several set-theoretic principles about

**Determinacy**Theorem - Stronger Forms of**Determinacy**... Several set-theoretic principles about

**determinacy**stronger than Borel**determinacy**are studied in descriptive set theory ... The axiom of projective**determinacy**states that all projective subsets of a Polish space are determined ... The axiom of**determinacy**states that all subsets of all Polish spaces are determined ...Mirror Mount - Related Devices

... designed based on the principles of kinematic

... designed based on the principles of kinematic

**determinacy**... A linear motion bearing or linear stage having kinematic**determinacy**uses two V-grooves sliding on a cylinder, a flat surface sliding on a second parallel ... For kinematic**determinacy**each leg consists of a ball set in a trihedral hole in the fixed frame, a ball joining a flat plate in the fixed frame, and a ball joing a trihedral ...Borel

... In descriptive set theory, the Borel

**Determinacy**Theorem... In descriptive set theory, the Borel

**determinacy**theorem states that any Gale-Stewart game whose winning set is a Borel set is determined, meaning that one of the two players will have a winning ... Later results showed that stronger**determinacy**theorems cannot be proven in Zermelo-Fraenkel set theory, although they are relatively consistent with it ...Related Subjects

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