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International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 14, Pages 2207-2215
http://dx.doi.org/10.1155/IJMMS.2005.2207

A notion of functional completeness for first-order structure

1Department of Mathematics, École Normale Supérieure, University of Yaoundé-1, P.O. Box 47, Yaoundé, Cameroon
2Department of Mathematics, Faculty of Science, University of Yaoundé-1, P.O. Box 812, Yaoundé, Cameroon

Received 27 September 2004; Revised 4 July 2005

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.