THE GAME OPERATOR ACTING ON WADGE CLASSES OF BOREL SETS

We study the behavior of the game operator Ə on Wadge classes of Borel sets. In particular we prove that the classical Moschovakis results still hold in this setting. We also characterize Wadge classes Γ for which the class ƏΓ has the substitution property. An effective variation of these results shows that for all 1 ≤ η < ω 1 CK and 2 ≤ ξ < ω 1 CK , Ə ( D η ( ∑ ξ 0 ) ) is a Spector class while Ə ( D 2 ( ∑ 1 0 ) ) is not.