First-order queries on databases embedded in an infinite structure

Abstract

We consider "generic" (isomorphism-invariant) queries on relational databases embedded in an infinite background structure. Assume a generic query is expressible by a first-order formula over the embedded domain that may involve both the relations of the database and the relations and functions of the background structure. Then this query is already expressible by a first-order formula involving just an auxiliary linear ordering as background structure. We present an elementary proof of this fact.