P-NDOP and P-decompositions of ℵ_ε-saturated models of superstable theories

Given a complete, superstable theory, we distinguish a class P of regular types, typically closed under automorphisms of C and non-orthogonality. We define the notion of P-NDOP, which is a weakening of NDOP. For superstable theories with P-NDOP, we prove the existence of P-decompositions and derive an analog of the first author's result in Israel J. Math. 140 (2004). In this context, we also -and a sucient condition on P-decompositions that implies non-isomorphic models. For this, we investigate natural structures on the types in P ∩ S(M) modulo non-orthogonality.