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Descriptive set theory studies definable subsets of spaces such as the Baire space of sequences, with particular emphasis on hierarchies of complexity, regularity properties and infinite games.

An infinite game of perfect information is determined when one of its two players has a winning strategy in an infinite game.

For a payoff set $A\subseteq M^{\omega }$, a quasistrategy for a player assigns a nonempty subset of $M$ to every finite position at which that player moves. A play is consistent with it when each of that player's moves belongs to the assigned set. The set $A$, or equivalently the infinite game of perfect information $G(A)$, is quasidetermined when one player has a quasistrategy under which every consistent play is won by that player.

Projective determinacy states that every infinite game of perfect information whose payoff is a projective set is determined.

An infinite game of perfect information is quasidetermined when one of the players has a winning quasistrategy. Choosing one allowed move at every relevant position refines a winning quasistrategy to a winning strategy in an infinite game whenever the required restricted choice principle holds.