Relational systems with trivial endomorphisms and polymorphisms (Q762526)

A finitary relation \(\rho\) and a finitary function \({\mathfrak f}\) on some set A are said to be compatible one with the other if \(\rho\) is a subalgebra of a suitable direct power of (A,\({\mathfrak f})\). In this paper properties for relational systems (A,Q) are derived in order to guarantee that every (finitary) function compatible with all relations of Q must be a projection or constant. The connection to interpolation properties is demonstrated and some open problems are stated.