Duality for finite Hilbert algebras

Sergio Celani,Leonardo Cabrer

doi:10.1016/j.disc.2005.09.002

Duality for finite Hilbert algebras

Sergio Celani, Leonardo Cabrer

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https://doi.org/10.1016/j.disc.2005.09.002

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Journal: Discrete Mathematics	Publication Date: Nov 28, 2005
Citations: 10	License type: publisher-specific-oa

Affiliation: Universidad Nacional del Centro de la Provincia de Buenos Aires, Consejo Nacional de Investigaciones Científicas y Técnicas

#Duality For Algebras #Finite Algebras + Show 4 more

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Abstract

In this work we shall give a characterization of the Hilbert algebras given by the order and we will prove a duality for finite Hilbert algebras by means of finite ordered sets endowed with a distinguished set of subsets. We will also study the case when the finite Hilbert algebras are join-semilattices or meet-semilattices relative to the natural order defined by the implication. Finally we will prove that Hilbert do not admit a natural duality.

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