RT Journal Article
T1 The dp-rank of abelian groups
A1 Halevi, Yatir
A1 Palacín Cruz, Daniel
AB An 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.
PB Cambridge University Press
SN 0022-4812
SN 1943-5886
YR 2019
FD 2019-02-01
LK https://hdl.handle.net/20.500.14352/98555
UL https://hdl.handle.net/20.500.14352/98555
LA eng
NO Halevi, 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.
DS Docta Complutense
RD 26 abr 2025