Unidimensional theories are superstable

doi:10.1016/0168-0072(90)90046-5

Annals of Pure and Applied Logic

Volume 50, Issue 2, 30 November 1990, Pages 117-137

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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 (sufficiently large) 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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^☆: |This work was part of the author's Ph.D. thesis under Professor Leo Harrington (Berkeley 1986). It was supported by an NSF graduate fellowship.

Annals of Pure and Applied Logic

Unidimensional theories are superstable☆

Abstract