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On some classes of Heyting algebras with successor that have the amalgamation property
(Springer, 2012-11)
In this paper we shall prove that certain subvarieties of the variety of Salgebras (Heyting algebras with successor) has amalgamation. This result together with an appropriate version of Theorem 1 of [L. L. Maksimova, ...
On the variety of Heyting algebras with successor generated by all finite chains
(Jagiellonian University Press, 2010-03)
Contrary to the variety of Heyting algebras, finite Heyting algebras with successor only generate a proper subvariety of that of all Heyting algebras with successor. In particular, all finite chains generate a proper ...
Discrete duality for TSH-algebras
(Korean Mathematical Society, 2012-08)
In this article, we continue the study of tense symmetric Heyting algebras (or TSH-algebras). These algebras constitute a generalization of tense algebras. In particular, we describe a discrete duality for TSH-algebras ...
A Categorical Equivalence for Tense Nelson Algebras
(Springer, 2021-08)
In this paper we present a category equivalent to that of tense Nelson algebras.The objects in this new category are pairs consisting of an IKt-algebra and a Boolean IKtcongruenceand the morphisms are a special kind of ...
Principal and boolean congruences on IKt-Algebras
(Springer, 2018-02)
The IKt-algebras were introduced in the paper An algebraic axiomatization of the Ewald’s intuitionistic tense logic by the first and third author. In this paper, our main interest is to investigate the principal and Boolean ...
Subdirectly Irreducible IKt-Algebras
(Kluwer Academic/Plenum Publ, 2017-02)
The IKt-algebras that we investigate in this paper were introduced in the paper "An algebraic axiomatization of the Ewald’s intuitionistic tense logic" by the first and third author. Now we characterize by topological ...
Free three-valued Closure Lukasiewicz Algebras
(Jagiellonian University Press, 2007-12)
In this paper, the structure of finitely generated free objects in the variety of three-valued closure Lukasiewicz algebras is determined. We describe their indecomposable factors and we give their cardinality.
Dually hemimorphic semi-Nelson algebras
(Oxford University Press, 2019-11)
Extending the relation between semi-Heyting algebras and semi-Nelson algebras to dually hemimorphic semi-Heyting algebras, we introduce and study the variety of dually hemimorphic semi-Nelson algebras and some of its ...
Constructive logic with strong negation as a substructural logic
(Oxford University Press, 2010-08)
Spinks and Veroff have shown that constructive logic with strong negation (CLSN for short), can be considered as a substructural logic. We use algebraic tools developed to study substructural logics to investigate some ...
Variations of the free implicative semilattice extension of a Hilbert algebra
(Springer Verlag Berlín, 2019-07)
Celani and Jansana (Math Log Q 58(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. ...