Weak systems of relations
by
Ferdinand Börner
Universität Potsdam

A set of relations on a basic set A is called a weak system if it contains the full relations A^m and if it is closed under intersection and closed under argument transformations (permutation and identification of arguments, addition of fictitious arguments).

Weak systems (with additional properties) appear as relational counterparts of clones of total or partial functions or hyperfunctions with respect to some Galois connections. But weak systems can also be characterized as the domain sets of the partial functions of a partial clone.

In the talk we discuss abstract properties of such systems, and we investigate some properties of the lattice of all weak systems on A.

Date received: May 24, 2004