# Determinacy

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.

### Other articles related to "determinacy":

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 ... Later results showed that stronger determinacy theorems cannot be proven in Zermelo-Fraenkel set theory, although they are relatively consistent with it ...
Axioms Of Set Theory - Areas of Study - 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 ... 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 real line are well behaved (i ...
Determinator - Determinacy and Large Cardinals - Projective Determinacy
... 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 ...
Borel 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
... by a semi gimbal mount most rotation stages are not designed based on the principles of kinematic determinacy ... or linear stage having kinematic determinacy uses two V-grooves sliding on a cylinder, a flat surface sliding on a second parallel cylinder, and a flat surface joining the screw ... 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 ...