SAS

Abstract

The accepted wisdom is that standard techniques from classical model theory fail to apply in the finite. We attempt to dispel this notion by presenting new proofs of the Gaifman and Hanf locality theorems, as they appear in Libkin's textbook on finite model theory. In particular, using compactness over an expanded vocabulary, we obtain strikingly simple arguments that apply over both finite and infinite structures -- all without the complexity of Ehrenfeucht–Fraïssé games normally used. Our techniques rely on internalizing most of the relevant mathematical features into the first-order theory itself. It remains to be seen whether these methods can be extended to proving order-invariant locality.