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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Citations of this work

Product of invariant types modulo domination–equivalence.Rosario Mennuni - 2020 - Archive for Mathematical Logic 59 (1):1-29.
Meager forking.Ludomir Newelski - 1994 - Annals of Pure and Applied Logic 70 (2):141-175.

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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.
Almost orthogonal regular types.Ehud Hrushovski - 1989 - Annals of Pure and Applied Logic 45 (2):139-155.
The geometry of weakly minimal types.Steven Buechler - 1985 - Journal of Symbolic Logic 50 (4):1044-1053.

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