Lightface analytic game

In descriptive set theory, a lightface analytic game is a game whose payoff set A is a [math]\displaystyle{ \Sigma^1_1 }[/math] subset of Baire space; that is, there is a tree T on [math]\displaystyle{ \omega\times\omega }[/math] which is a computable subset of [math]\displaystyle{ (\omega\times\omega)^{\lt \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^#.