Determinacy

property of sets in a topological space that differ from open sets by meager sets

large cardinal number that is the critical point of a nontrivial elementary embedding of the universe into a transitive class

set-theoretic statement, consistent with ZF but contradicting choice, that any game corresponding to a subset of Baire space is determined

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.