  In fact by modifying the above proofs one can obtain the regularity properties for a larger pointclass, namely, ∃ℝΓ. This is the pointclass obtained by taking projections of sets in Γ. So, for example, if Γ is Δ̰11 then ∃ℝΓ is Σ̰11. It follows that assuming Δ̰11-determinacy (which is provable in ZFC) one gets that the Σ̰11 sets of reals have the regularity properties (see the exercises in 6.G of Moschovakis (1980)). In this sense determinacy lies at the heart of the regularity properties and may be considered their true source. 