Variations of the free implicative semilattice extension of a Hilbert algebra

CASTIGLIONI, JOSÉ L.; SAN MARTÍN, HERNÁN J.

Soft Computing

Springer-Nature

Año: 2018

1432-7643

Celani and Jansana (Math LogQ58(3):188?207, 2012) give an explicit description of the free implicative semilattice extension of a Hilbert algebra. In this paper, we give an alternative path conducing to this construction. Furthermore, following our procedure, we show that an adjunction can be obtained between the algebraic categories of Hilbert algebras with supremum and that of generalized Heyting algebras. Finally, in the last section, we describe a functor from the algebraic category of Hilbert algebras to that of generalized Heyting algebras, of possible independent interest.