English

Some model-theoretic consequences of high-arity uniform convergence, part I

Logic 2026-05-12 v1

Abstract

We show that certain families of sets in R2\mathbb{R}^2 (or Rn\mathbb{R}^n) which are neither definable nor have bounded VC-dimension are nonetheless uniformly approximately definable in the real field, an o-minimal structure.

Keywords

Cite

@article{arxiv.2605.09911,
  title  = {Some model-theoretic consequences of high-arity uniform convergence, part I},
  author = {Leonardo N. Coregliano and Maryanthe Malliaris},
  journal= {arXiv preprint arXiv:2605.09911},
  year   = {2026}
}

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19 pages