Amalgamation in quasivarieties of Sugihara algebras

Abstrakt

Recent years have witnessed our understanding of amalgamation in residuated structures expand very rapidly, with the most notable successes focusing on varieties of residuated lattices. In the present work, we give a complete classification of subquasivarieties of Sugihara algebras with the amalgamation property. This extends the state of the art in two directions. First, it provides an entry point toward such classification theorems in the setting of quasivarieties, whereas heretofore available classification results of this sort dealt only with subvarieties of certain varieties of residuated structures. Second, it offers a foray into the study of amalgamation in constant-free analogues of residuated lattices, whose theory is more difficult in several respects, due primarily to the more complicated theory of congruences in the constant-free setting. As arbitrary quasivarieties of Sugihara algebras lack the congruence extension property — which has often proven a key ingredient in studies of amalgamation in residuated lattices — these results may also hint at some general methods that may prove useful in the study of amalgamation when the congruence extension property is absent.