  For a pointclass Γ of (k-tuples of) sets of reals, let Det(Γ) be the statement that all sets of reals in Γ are determined. In what follows we shall assume that Γ has certain minimal closure properties; more precisely, we shall assume that Γ is an adequate pointclass in the sense of Moschovakis (1980). The precise details of this notion are not important for our purposes; suffice it to say that all of the pointclasses introduced thus far are adequate. 