A notion of functional completeness for first-order structure

Using ☆-congruences and implications, Weaver (1993) introduced the concepts of prevariety and quasivariety of first-order structures as generalizations of the corresponding concepts for algebras. The notion of functional completeness on algebras has been defined and characterized by Burris and Sankappanavar (1981), Kaarli and Pixley (2001), Pixley (1996), and Quackenbush (1981). We study the notion of functional completeness with respect to ☆-congruences. We extend some results on functionally complete algebras to first-order structures A=(A;FA;RA) and find conditions for these structures to have a compatible Pixley function which is interpolated by term functions on suitable subsets of the base set A