Halevi, YatirPalacín Cruz, Daniel2024-02-032024-02-032019-02-01Halevi, Y.; Palacín, D. THE DP-RANK OF ABELIAN GROUPS. The Journal of Symbolic Logic 2019, 84(3), 957–986. doi:10.1017/jsl.2018.89.0022-48121943-588610.1017/jsl.2018.89https://hdl.handle.net/20.500.14352/98555An equation to compute the dp-rank of any abelian group is given. It is also shown that its dp-rank, or more generally that of any one-based group, agrees with its Vapnik–Chervonenkis density. Furthermore, strong abelian groups are characterised to be precisely those abelian groups A such that there are only finitely many primes p such that the group A/pA is infinite and for every prime p, there are only finitely many natural numbers n such that (p^n A)[p]/(p^{n + 1} A)[p] is infinite. Finally, it is shown that an infinite stable field of finite dp-rank is algebraically closed.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/journal articlehttps//doi.org/10.1017/jsl.2018.89open accessAbelian groupOne-basedVc-densityDp-rankLógica simbólica y matemática (Matemáticas)1102.10 Teoría de Modelos