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arXiv · 1912.12279

A rank based on Shelah trees

Santiago Cárdenas-Martín·Rafel Farré
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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.

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Santiago Cárdenas-Martín, Rafel Farré. 2022-02-15. A rank based on Shelah trees. https://arxiv.org/abs/1912.12279

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