Classes of finite relations as initial abstract data types. I (Q1179266)

It is known that the finite functions and the finite partial functions form the initial algebraic theory and the initial pointed algebraic theory, respectively. The authors prove a similar result for a poorer algebraic structure. Axiomatizations for sixteen types of finite relations are given. These classes of relations are intersections of the following four basic classes of relations: total relations, surjective relations, partial functions and injective relations.