English

On VC-minimal fields and dp-smallness

Logic 2013-07-31 v1

Abstract

In this paper, we show that VC-minimal ordered fields are real closed. We introduce a notion, strictly between convexly orderable and dp-minimal, that we call dp-small, and show that this is enough to characterize many algebraic theories. For example, dp-small ordered groups are abelian divisible and dp-small ordered fields are real closed.

Cite

@article{arxiv.1307.8004,
  title  = {On VC-minimal fields and dp-smallness},
  author = {Vincent Guingona},
  journal= {arXiv preprint arXiv:1307.8004},
  year   = {2013}
}

Comments

17 pages

R2 v1 2026-06-22T01:00:30.654Z