Colourings, generics, and free amalgams

Abstract

We study free amalgamation classes over a finite relational language and their applications to the model companions of 'v 1 classes over a finite relational language.

If an 'v 1 class K is a free amalgamation class over a finite relational language with edges, the model companion os nqfa(1): non-finitely axiomatizable een modulo axioms asserting "I embed all finite structures in K". Further, there is a structure in K isometrically embedding each countable structure in K (relative to the least path metric on the graphs of structures in K).

We study colour classes in 'v 1 free amalgamation classes over a finite relational language and their model companions. We find sufficient conditions for the model companion of a colour class to exist: when the model companion exists, it has a theory equal to the theory of a generic structure and is nqfa(1).