Baker–Pixley theorem for algebras in relatively congruence distributive quasivarieties

Abstract

A classical theorem of Baker and Pixley states that if [Formula: see text] is a finite algebra with a majority term and [Formula: see text] is an [Formula: see text]-ary operation on [Formula: see text] which preserves every subuniverse of [Formula: see text], then [Formula: see text] is representable by a term in [Formula: see text]. We give a generalizacion of this theorem for the case in which [Formula: see text] is a finite algebra belonging to some relatively congruence distributive quasivariety.