2017/06/17 by Rafel Farré, Farré, Rafel · 1 citation
Computer Science · Mathematics · #03C45 03C64 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1706.05471
openalex publication_date 2017/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.