Relational clone

Summary

A relational clone on a set $A$ is a set of finitary relations on $A$ that is closed under primitive positive definitions. It must also contain the equality relation and the empty relation. Primitive positive definitions are those that use only conjunction, existential quantification and equality. Relational clones are dual to clones of operations. On a finite set, the operators $\operatorname{Pol}$ and $\operatorname{Inv}$ give a bijection between them. Another common name is co-clone.