Vapnik-Chervonenkis density in some theories without the independence property, II

TL;DR

This paper investigates the VC density in specific stable first-order theories, providing uniform bounds in finite U-rank theories without the finite cover property and characterizing abelian groups with bounded VC density.

Contribution

It offers new uniform bounds on VC density in certain stable theories and characterizes abelian groups with bounded VC density, advancing understanding in model theory.

Findings

Established uniform VC density bounds in finite U-rank theories without FCP

Characterized abelian groups with uniform VC density bounds

Contributed to the understanding of VC density in stable theories

Abstract

We study the Vapnik-Chervonenkis (VC) density of definable families in certain stable first-order theories. In particular we obtain uniform bounds on VC density of definable families in finite U-rank theories without the finite cover property, and we characterize those abelian groups for which there exist uniform bounds on the VC density of definable families.