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This paper is a sequel to  and it contains, among other things, proofs of the results announced in the last section of that paper. In §1, we use the general method of  together with reflection arguments to study the properties of forcing with Δ perfect trees, for certain Spector pointclasses Γ, obtaining as a main result the existence of a continuum of minimal Δ-degrees for such Γ's, under determinacy hypotheses. In particular, using PD, we prove the existence of continuum many minimal Δ½doi:10.2307/2273229 fatcat:ignwrzjdsre6dhoe454yv37u54