VC-Density in Pairs of Ordered Vector Space
Logic
2026-01-06 v3
Abstract
We show that the VC-density of any partitioned formula in a pair of ordered vector spaces is bounded above by twice the number of parameter variables. We also show that this bound is optimal and, as a by-product, we prove that no dense pair of o-minimal structures is dp-minimal.
Cite
@article{arxiv.2405.10069,
title = {VC-Density in Pairs of Ordered Vector Space},
author = {Ayhan Günaydın and Ebru Nayir},
journal= {arXiv preprint arXiv:2405.10069},
year = {2026}
}