Lightface analytic game

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