2013/11/16 by Ziv Shami, Shami, Ziv
Economics, Econometrics and Finance · Mathematics · Medicine · #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #Pituitary Gland Disorders and Treatments #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1311.4053
openalex publication_date 2013/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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).