P-NDOP and P-decompositions of $ℵ_{ϵ}$-saturated models of superstable theories

• Autorzy: Saharon Shelah , Michael C. Laskowski
• Języki publikacji: EN

Abstrakty

EN

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 find a sufficient 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.

Kategorie tematyczne

• 03C50: Models with special properties (saturated, rigid, etc.)
• 03C45: Classification theory, stability and related concepts

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2015
• Tom: 229
• Numer: 1
• Strony: 47-81

Daty

wydano

2015

Twórcy

autor

Saharon Shelah

• Einstein 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.

autor

Michael C. Laskowski

• Department of Mathematics, University of Maryland, College Park, MD 20742, U.S.A.

Identyfikatory

DOI

10.4064/fm229-1-2