Unidimensional theories are superstable

Annals of Pure and Applied Logic 50 (2):117-137 (1990)
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Abstract

A first order theory T of power λ is called unidimensional if any twoλ+-saturated models of T of the same cardinality are isomorphic. We prove here that such theories are superstable, solving a problem of Shelah. The proof involves an existence theorem and a definability theorem for definable groups in stable theories, and an analysis of their relation to regular types.

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10.1016/0168-0072(90)90046-5

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Unidimensional theories are superstable.Ehud Hrushovski - 1990 - Annals of Pure and Applied Logic 50 (2):117-137.
Review: Ehud Hrushovski, Unidimensional Theories are Superstable; Ehud Hrushovski, Almost Orthogonal Regular Types. [REVIEW]Frank Wagner - 1992 - Journal of Symbolic Logic 57 (2):762-763.
BURKE, MR and MAGIDOR, M., Shelah's pcf theory and its applications EDA, K., Boolean powers of abelian groups HRUSHOVSKI, E., Unidimensional theories are superstable. [REVIEW]H. Judah - 1990 - Annals of Pure and Applied Logic 50:303.
Ehud Hrushovski. Unidimensional theories are superstable. Annals of pure and applied logic, vol. 50 , pp. 117–138. - Ehud Hrushovski. Almost orthogonal regular types. Annals of pure and applied logic, vol. 45 , pp. 139–155. [REVIEW]Frank Wagner - 1992 - Journal of Symbolic Logic 57 (2):762-763.
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References found in this work

On strongly minimal sets.J. T. Baldwin & A. H. Lachlan - 1971 - Journal of Symbolic Logic 36 (1):79-96.
Superstable groups.Ch Berline & D. Lascar - 1986 - Annals of Pure and Applied Logic 30 (1):1-43.
Une théorie de galois imaginaire.Bruno Poizat - 1983 - Journal of Symbolic Logic 48 (4):1151-1170.
The geometry of weakly minimal types.Steven Buechler - 1985 - Journal of Symbolic Logic 50 (4):1044-1053.
Almost orthogonal regular types.Ehud Hrushovski - 1989 - Annals of Pure and Applied Logic 45 (2):139-155.

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