Superstable theories with few countable models

Archive for Mathematical Logic 31 (6):457-465 (1992)
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Abstract

We prove here:Theorem. LetT be a countable complete superstable non ω-stable theory with fewer than continuum many countable models. Then there is a definable groupG with locally modular regular generics, such thatG is not connected-by-finite and any type inG eq orthogonal to the generics has Morley rank.Corollary. LetT be a countable complete superstable theory in which no infinite group is definable. ThenT has either at most countably many, or exactly continuum many countable models, up to isomorphism

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Citations of this work

Meager forking.Ludomir Newelski - 1994 - Annals of Pure and Applied Logic 70 (2):141-175.
On the number of models of uncountable theories.Ambar Chowdhury & Anand Pillay - 1994 - Journal of Symbolic Logic 59 (4):1285-1300.

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References found in this work

The geometry of weakly minimal types.Steven Buechler - 1985 - Journal of Symbolic Logic 50 (4):1044-1053.
Kueker's conjecture for stable theories.Ehud Hrushovski - 1989 - Journal of Symbolic Logic 54 (1):207-220.
A dichotomy theorem for regular types.Ehud Hrushovski & Saharon Shelah - 1989 - Annals of Pure and Applied Logic 45 (2):157-169.
An Introduction to Stability Theory.Anand Pillay - 1986 - Journal of Symbolic Logic 51 (2):465-467.

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