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

TL;DR

This paper introduces P-NDOP and P-decompositions for superstable theories, providing new tools to analyze model structures and conditions for non-isomorphic models, extending classical results in stability theory.

Contribution

It defines P-NDOP and establishes the existence of P-decompositions, extending the analysis of superstable models and deriving an analog of Shelah's result for these theories.

Findings

Established P-NDOP for superstable theories.

Proved existence of P-decompositions.

Identified conditions for non-isomorphic models.

Abstract

Assume a complete superstable theory is superstable, and let P be a class of regular types, typically closed under automorphisms of the monster and non-orthogonality. We define the notion of P-NDOP and prove the existence of P-decompositions and derive an analog of Sh401 for superstable theories with P-NDOP. In this context, we also find a sufficient condition on P-decompositions that imply non-isomorphic models. For this, we investigate natural structures on the types in P\intersect S(M) modulo non-orthogonality.