In descriptive set theory, a lightface analytic game is a game whose payoff set A is a <math>\Sigma^1_1</math> subset of Baire space; that is, there is a tree T on <math>\omega\times\omega</math> which is a computable subset of <math>(\omega\times\omega)^{<\omega}</math>, such that A is the projection of the set of all branches of T. The determinacy of all lightface analytic games is equivalent to the existence of 0#.
