2018/07/05 by José Luis Castiglioni, Castiglioni, José L., Hernán Javier San Martín +1
Computer Science · #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Rough Sets and Fuzzy Logic
paper · doi:10.48550/arxiv.1807.02423
openalex publication_date 2018/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In [\it On the free implicative semilattice extension of a Hilbert algebra. Mathematical Logic Quarterly 58, 3 (2012), 188--207], Celani and Jansana 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 last section we describe a functor from the algebraic category of Hilbert algebras to that of generalized Heyting algebras, of possible independent interest.