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A dichotomy for D-rank 1 types in simple theories

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Abstract

We prove a dichotomy for D-rank 1 types in simple theories that generalizes Buechler’s dichotomy for D-rank 1 minimal types in stable theories: every D-rank 1 type is either 1-based or part of its algebraic closure, defined 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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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Ariel University, Samaria, Ariel, 44873, Israel

    Ziv Shami

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  1. Ziv Shami
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Correspondence to Ziv Shami.

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Shami, Z. A dichotomy for D-rank 1 types in simple theories. Isr. J. Math. 209, 993–1012 (2015). https://doi.org/10.1007/s11856-015-1243-z

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  • DOI: https://doi.org/10.1007/s11856-015-1243-z

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