Publications > Preprint server > Preprint Number 816
Preprint Number 816
816. Domenico Zambella
Elementary classes of finite VC-dimension
Submission date: 18 December 2014.
Let U be a monster model and let D be a subset of U. Let (U,D) denote the expansion 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).
Mathematics Subject Classification:
Keywords and phrases:
|Last updated: January 5 2015 18:35||Please send your corrections to:|