Submission date: 12 December 2017

Abstract:

An equation to compute the dp-rank of any abelian group is given. It is also shown that its dp-rank, or more generally 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 the subgroup pA has infinite index for only finitely many primes.
Finally, it is shown that an infinite stable field of finite dp-rank is algebraically closed.

Mathematics Subject Classification:

Keywords and phrases:

Full text arXiv 1712.04503: pdf, ps.