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arXiv · 2604.27816

VC-Density in Divisible Oriented Abelian Groups and Their Pairs

Ebru Nayir·Melissa Özsahakyan
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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.

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Ebru Nayir, Melissa Özsahakyan. 2026-04-30. VC-Density in Divisible Oriented Abelian Groups and Their Pairs. https://arxiv.org/abs/2604.27816

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