Submission date: 27 December 2019

Abstract:

We define a global rank for partial types based in a generalization of Shelah trees. We prove an equivalence with the depth of a localized version of the constructions known as dividing sequence and dividing chain. This rank characterizes simple and supersimple types. Moreover, this rank does not change for non-forking extensions under certain hypothesys. We also prove this rank satisfies Lascar-style inequalities. As an application, we provide a partial answer to a question posed in Chernikov[4].

Mathematics Subject Classification:

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Full text arXiv 1912.12279: pdf, ps.