The boole-de morgan correspondence: 1842–1864

De Morgan Triples Revisited

In this paper we overview basic known results about the varieties generated by De Morgan triples and about the problem to find equations defining the variety generated by a concrete De Morgan triple. We also provide some alternative proofs and some new results, specially for the case of Łukasiewicz De Morgan triples.

Utilisation de l'algèbre de Boole en logique mathématique

Dually quasi-De Morgan Stone semi-Heyting algebras II. Regularity

This paper is the second of a two part series. In this Part, we prove, using the description of simples obtained in Part I, that the variety $mathbf{RDQDStSH_1}$ of regular dually quasi-De Morgan Stone semi-Heyting algebras of level 1 is the join of the variety generated by the twenty 3-element $mathbf{RDQDStSH_1}$-chains and the variety of dually quasi-De Morgan Boolean semi-Heyting algebras--...

Dually quasi-De Morgan Stone semi-Heyting algebras I. Regularity

This paper is the first of a two part series. In this paper, we first prove that the variety of dually quasi-De Morgan Stone semi-Heyting algebras of level 1 satisfies the strongly blended $lor$-De Morgan law introduced in cite{Sa12}. Then, using this result and the results of cite{Sa12}, we prove our main result which gives an explicit description of simple algebras(=subdirectly irreducibles) ...

Contact relation on De Morgan algebra

In the paper, the notion of a contact relation on de Morgan algebra is defined, the algebraic structure of all contact relations and the connection to the set of all close, reflexive and symmetric relations on all maximal filters are investigated. 2010 AMS Classification: 06D30, 06F30, 54E05, 54H12