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

Saharon Shelah¹ ; Michael C. Laskowski²

¹ Einstein 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 110 Frelinghuysen Road Piscataway, NJ 08854-9019, U.S.A.
² Department of Mathematics University of Maryland College Park, MD 20742, U.S.A.

Fundamenta Mathematicae, Tome 229 (2015) no. 1, pp. 47-81.

Résumé

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.

Détail

DOI : 10.4064/fm229-1-2

Keywords: given complete superstable theory distinguish class mathbf regular types typically closed under automorphisms mathfrak non orthogonality define notion mathbf ndop which weakening ndop superstable theories mathbf ndop prove existence mathbf decompositions derive analog first authors result israel nbsp math context sufficient condition mathbf decompositions implies non isomorphic models investigate natural structures types mathbf cap modulo non orthogonality