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## $\mathbf P$-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.

#### Autorzy

• Saharon ShelahEinstein Institute of Mathematics
The Hebrew University of Jerusalem
Edmond J. Safra Campus, Givat Ram
Jerusalem, 91904, Israel
and
Department of Mathematics
Hill Center, Busch Campus
Rutgers, the State University of New Jersey
Piscataway, NJ 08854-9019, U.S.A.
e-mail
• Michael C. LaskowskiDepartment of Mathematics
University of Maryland
College Park, MD 20742, U.S.A.
e-mail

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