On prelinear Hilbert algebras with successor

Abstract

In this paper we give an explicit description of the left adjoint of the forgetful functor from the algebraic category of Gödel algebras with successor to the algebraic category of bounded prelinear Hilbert algebras with successor. We apply this result in order to study possible descriptions of the coproduct of two finite algebras in the algebraic category of prelinear Hilbert algebras with successor.