$\mathbf P$-NDOP and $\mathbf P$-decompositions of $\aleph _{\epsilon} $-saturated models of superstable theories

Volume 229 / 2015

Saharon Shelah, Michael C. Laskowski Fundamenta Mathematicae 229 (2015), 47-81 MSC: Primary 03C45; Secondary 03C50. DOI: 10.4064/fm229-1-2


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.


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

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