Lightface analytic game

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