The envelope of a pointclass under a local determinacy hypothesis

Given an inductive-like pointclass Γ˜ and assuming the Axiom of Determinacy, Martin identified and analyzed a pointclass that contains the prewellorderings of the next scale beyond Γ˜ if such a scale exists. We show that much of Martin's analysis can be carried out assuming only ZF+DCRZF+DCR and Δ˜Γ˜ determinacy by adapting arguments of Kechris and Woodin [10] and Martin [13]. This generalization can be used to show that every set of reals is Suslin in the intersection of two divergent models of AD+AD+, giving a new proof of a theorem of Woodin, as well as to show that every set of reals is Suslin in the derived model at an indestructibly weakly compact limit of Woodin cardinals.