 For definiteness, when we speak of the “structure theory” (at a given level) we shall be referring to the regularity properties introduced above—the perfect set property, and the property of Baire, and Lebesgue measurability—along with the uniformization property. There is actually much more (as indicated above) to the structure theory and what we shall have to say generalizes. We shall concentrate on two levels of definable determinacy—Δ̰11-determinacy and ADL(ℝ). Again, this is just for definiteness and what we shall have to say generalizes to certain higher forms of definable determinacy. 