Amalgamation Theorems in Algebraic Logic, an overview

Abstract

We review, and in the process unify two techniques (due to Németi and Pigozzi), for proving results concerning amalgamation in several classes studied in algebraic logic. The logical counterpart of these results adress interpolation and definability properties in modal and algebraic logic. Presenting them in a functorial context as adjoint situations, we show that both techniques can indeed be seen as instances of the use of the Keisler-Shelah ultrapower Theorem in proving Robinson's Joint Consistency Theorem. Some new results are surveyed. The results of this paper are presented in such a way that further establishes the hitherto existing well developed duality theory between boolean algebras with operators and modal logic.