An Ehrenfeucht-Fraïssé Approach to Collapse Results for First-Order Queries over Embedded Databases

We present a new proof technique for collapse results for first–order queries on databases which are embedded in N or R>0. Our proofs are by means of an explicitly constructed winning strategy for Duplicator in an Ehrenfeucht–Fräıssé game, and can deal with certain infinite databases where previous, highly involved methods fail. Our main result is that first–order logic has the natural–generic collapse over 〈N, 6 , +〉 for arbitrary (i.e., possibly infinite) databases. Furthermore, a first application of this result shows the natural–generic collapse of first–order logic over 〈R>0, 6, +〉 for a certain kind of databases over R>0 which consist of a possibly infinite number of regions. Classification: Logic in Computer Science, Database Theory.