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