Submission date: 16 November 2013

Abstract:

We prove a dichotomy for D-rank 1 types in simple theories that generalizes Buechler's dichotomy for D-rank 1 minimal types: every such type is either 1-based or its algebraic closure, by a single formula, almost contains a non-algebraic formula that belongs to a non-forking extension of the type. In addition we prove that a densely-1 based type of D-rank 1 is 1-based. We also observe that for a hypersimple unidimensional theory the existence of a non-algebraic stable type implies stability (and thus superstability).

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Full text arXiv 1311.4053: pdf, ps.