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.