A rank based on Shelah trees
Logic
2022-02-16 v5
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.
Cite
@article{arxiv.1912.12279,
title = {A rank based on Shelah trees},
author = {Santiago Cárdenas-Martín and Rafel Farré},
journal= {arXiv preprint arXiv:1912.12279},
year = {2022}
}