English

On VC-minimal theories and variants

Logic 2011-10-20 v1

Abstract

In this paper, we study VC-minimal theories and explore related concepts. We first define the notion of convex orderablility and show that this lies strictly between VC-minimality and dp-minimality. Next, we define the notion of weak VC-minimality, show it lies strictly between VC-minimality and dependence, and show that all unstable weakly VC-minimal theories interpret an infinite linear order. Finally, we define the notion full VC-minimality, show that this lies strictly between weak o-minimality and VC-minimality, and show that theories that are fully VC-minimal have low VC-density.

Keywords

Cite

@article{arxiv.1110.4274,
  title  = {On VC-minimal theories and variants},
  author = {Vincent Guingona and Michael C. Laskowski},
  journal= {arXiv preprint arXiv:1110.4274},
  year   = {2011}
}

Comments

15 pages

R2 v1 2026-06-21T19:22:45.845Z