Duality for finite Hilbert algebras

AbstractIn this work we shall give a characterization of the Hilbert algebras given by the order and we will prove a duality for finite Hilbert algebras by means of finite ordered sets endowed with a distinguished set of subsets. We will also study the case when the finite Hilbert algebras are join-semilattices or meet-semilattices relative to the natural order defined by the implication. Finally we will prove that Hilbert do not admit a natural duality