English

Elementary classes of finite VC-dimension

Logic 2015-08-21 v2

Abstract

Let U be a monster model and let D be a subset of U. Let (U,D) denote theexpansion of U with a new predicate for D. Write e(D) for the collection of all subsets C of U such that (U,C) is elementary equivalent to (U,D). We prove that if e(D) has finite VC-dimension then D is externally definable (i.e. it is the trace on U of a set definable in an elementary superstructure of U).

Keywords

Cite

@article{arxiv.1412.5781,
  title  = {Elementary classes of finite VC-dimension},
  author = {Domenico Zambella},
  journal= {arXiv preprint arXiv:1412.5781},
  year   = {2015}
}

Comments

Small corrections

R2 v1 2026-06-22T07:36:33.959Z