Non-isolated types in stable theories

Annals of Pure and Applied Logic 145 (1):1-15 (2007)
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Abstract

We introduce notions of strong and eventual strong non-isolation for types in countable, stable theories. For T superstable or small stable we prove a dichotomy theorem: a regular type over a finite domain is either eventually strongly non-isolated or is non-orthogonal to a NENI type . As an application we obtain the upper bound for Lascar’s rank of a superstable theory which is one-based or trivial, and has fewer than 20 non-isomorphic countable models

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Citations of this work

Simple groups and the number of countable models.Predrag Tanović - 2013 - Archive for Mathematical Logic 52 (7-8):779-791.

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References found in this work

A new strongly minimal set.Ehud Hrushovski - 1993 - Annals of Pure and Applied Logic 62 (2):147-166.
ℵ0-Categorical, ℵ0-stable structures.G. Cherlin, L. Harrington & A. H. Lachlan - 1985 - Annals of Pure and Applied Logic 28 (2):103-135.
Almost orthogonal regular types.Ehud Hrushovski - 1989 - Annals of Pure and Applied Logic 45 (2):139-155.
Meager forking.Ludomir Newelski - 1994 - Annals of Pure and Applied Logic 70 (2):141-175.
A model and its subset.Ludomir Newelski - 1992 - Journal of Symbolic Logic 57 (2):644-658.

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