On the free Heyting algebra extension of a Hilbert algebra

J. L. Castiglioni, H. J. San Martín

Published 2017-05-10Version 1

In this paper we provided an explicit construction for the left adjoint of the forgetful functor from the category of Heyting algebras to that of Hilbert algebras. This functor factorizes through the free implicative semilattice extension of a Hilbert algebra of Celani and Jansana [On the free implicative semilattice extension of a Hilbert algebra}. Mathematical Logic Quarterly 58, 3 (2012), 188--207].