Variations of the free implicative semilattice extension of a Hilbert algebra
Logic
2018-07-09 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1807.02423,
title = {Variations of the free implicative semilattice extension of a Hilbert algebra},
author = {José L. Castiglioni and Hernán J. San Martín},
journal= {arXiv preprint arXiv:1807.02423},
year = {2018}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1705.03856