A rank based on Shelah trees

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.