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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm229-1-2,
author = {Saharon Shelah and Michael C. Laskowski},
title = {P-NDOP and P-decompositions of $\_{[?]}$-saturated models of superstable theories},
journal = {Fundamenta Mathematicae},
volume = {228},
year = {2015},
pages = {47-81},
zbl = {06401013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm229-1-2}
}
Saharon Shelah; Michael C. Laskowski. P-NDOP and P-decompositions of $ℵ_{ϵ}$-saturated models of superstable theories. Fundamenta Mathematicae, Tome 228 (2015) pp. 47-81. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm229-1-2/