$\mathbf P$-NDOP and $\mathbf P$-decompositions of $\aleph _{\epsilon} $-saturated models of superstable theories
Tom 229 / 2015
Fundamenta Mathematicae 229 (2015), 47-81
MSC: Primary 03C45; Secondary 03C50.
DOI: 10.4064/fm229-1-2
Streszczenie
Given a complete, superstable theory, we distinguish a class ${\mathbf P}$ of regular types, typically closed under automorphisms of ${\mathfrak C}$ and non-orthogonality. We define the notion of ${\mathbf P}$-NDOP, which is a weakening of NDOP. For superstable theories with ${\mathbf P}$-NDOP, we prove the existence of ${\mathbf P}$-decompositions and derive an analog of the first author's result in Israel J. Math. 140 (2004). In this context, we also find a sufficient condition on ${\mathbf P}$-decompositions that implies non-isomorphic models. For this, we investigate natural structures on the types in ${\mathbf P}\cap S(M)$ modulo non-orthogonality.
