Model completions and r-Heyting categories Original Research Article

Under some assumptions on an equational theory S (EDPC and EDPM), we give a necessary and sufficient condition so that S admits a model completion. These assumptions are often met by the equational theories arising from logic. They say that the dual of the category of finitely presented S-algebras has some categorical stucture. The results of this paper combined with those of [7] show that all the 8 theories of amalgamable varieties of Heyting algebras [12] admit a model completion. Further applications to varieties of modal algebras are given in [8].