The members of thin and minimal Π10 classes, their ranks and Turing degrees

We study the relationship among members of Π10 classes, thin Π10 classes, their Cantor–Bendixson ranks and their Turing degrees; in particular, we show that any nonzero Δ20 degree contains a member of rank α for any computable ordinal α  . Furthermore we observe that the degrees containing members of thin Π10 classes are not closed under join.