A hyperamalgamation property

The superamalgamation property is a strengthening of the amalgamation property and has found many applications in algebraic logic, more recently, also in model theory. Here we introduce an even stronger notion we call the hyperamalgamation property. We show that lattices, semilattices, Boolean algebras and dual Heyting algebras have the hyperamalgamation property. As a first application, we obtain the amalgamation property for semilattices, Boolean algebras and Heyting algebras with further operators.