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Preprint Number 1241
1241. Rafel Farré
Strong ordered Abelian groups and dp-rank
Submission date: 17 June 2017
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.
Mathematics Subject Classification: 03C45 03C64
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