Isolated types in a weakly minimal set

Journal of Symbolic Logic 52 (2):543-547 (1987)
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Theorem A. Let T be a small superstable theory, A a finite set, and ψ a weakly minimal formula over A which is contained in some nontrivial type which does not have Morley rank. Then ψ is contained in some nonalgebraic isolated type over A. As an application we prove Theorem B. Suppose that T is small and superstable, A is finite, and there is a nontrivial weakly minimal type p ∈ S(A) which does not have Morley rank. Then the prime model over A is not minimal over A



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Vaught’s conjecture for superstable theories of finite rank.Steven Buechler - 2008 - Annals of Pure and Applied Logic 155 (3):135-172.
Non-totally transcendental unidimensional theories.Anand Pillay & Philipp Rothmaler - 1990 - Archive for Mathematical Logic 30 (2):93-111.

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Locally modular theories of finite rank.Steven Buechler - 1986 - Annals of Pure and Applied Logic 30 (1):83-94.

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