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arXiv · 1706.05471

Strong ordered Abelian groups and dp-rank

Rafel Farré
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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 $n$. We also show the Dp-rank coincides with the Vapnik-Chervonenkis density.

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Rafel Farré. 2017-06-17. Strong ordered Abelian groups and dp-rank. https://arxiv.org/abs/1706.05471

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