Duality theorems for finite structures (characterising gaps and good characterisations)

We provide a correspondence between the subjects of duality and density in classes of finite relational structures. The purpose of duality is to chara cterise the structures C that do not admit a homomorphism into a given targ et B by the existence of a homomorphism from a structure A into C. Density is the older-theoretic property of containing no covers (or "gaps"). We sho w that the covers in the skeleton of a category of finite relational models correspond naturally to certain instances of duality statements, and we ch aracterise these covers. (C) 2000 Academic Press.