Abstract

In this survey article we present some of Janusz Czelakowski’s most influential contributions to the theory of quasivarieties. The material includes his work on: definability of principal congruences, characterizations of relative congruence distributivity, and equational definability of principal meets. In addition, we show how Czelakowski and Dziobiak applied these ideas to produce finite basis theorems. Special emphasis is placed on delivering a readable and self-contained account that incorporates the majority of the proofs and highlights the connections among the covered topics.