Abstract

In some varieties of algebras one can reduce the question of finding most general unifiers to the problem of the existence of unifiers that fulfil the additional condition called projectivity. In this article, we study this problem for Fregean varieties that arise from the algebraization of fragments of intuitionistic or intermediate logics. We investigate properties of Fregean varieties, guaranteeing either for a given unifiable term or for all unifiable terms, that projective unifiers exist. We indicate the identities which fully characterize congruence permutable Fregean varieties having projective unifiers and describe an effective procedure for finding such unifiers. In particular, we show that for a congruence permutable Fregean variety there exists the largest subvariety that has projective unifiers