VC-Density in Divisible Oriented Abelian Groups and Their Pairs
Logic
2026-05-01 v1
Abstract
We show that the VC-density in certain theories of oriented abelian groups is at most the size of parameter variables, which yields dp-minimality. We further prove that the VC-density of formulas in pairs of such models is bounded by twice the size of parameter variables. This uniform upper bound is shown to be sharp, and as a consequence, we show that such pairs have dp-rank 2.
Keywords
Cite
@article{arxiv.2604.27816,
title = {VC-Density in Divisible Oriented Abelian Groups and Their Pairs},
author = {Ebru Nayir and Melissa Özsahakyan},
journal= {arXiv preprint arXiv:2604.27816},
year = {2026}
}