Strong ordered Abelian groups and dp-rank
Logic
2017-06-20 v1
Abstract
We provide an algebraic characterization of strong ordered Abelian groups: An ordered Abelian group is strong iff it has bounded regular rank and almost finite dimension. Moreover, we show that any strong ordered Abelian group has finite Dp-rank. We also provide a formula that computes the exact valued of the Dp-rank of any ordered Abelian group. In particular characterizing those ordered Abelian groups with Dp-rank equal to . We also show the Dp-rank coincides with the Vapnik-Chervonenkis density.
Cite
@article{arxiv.1706.05471,
title = {Strong ordered Abelian groups and dp-rank},
author = {Rafel Farré},
journal= {arXiv preprint arXiv:1706.05471},
year = {2017}
}