A categorial equivalence for semi-Nelson algebras

Characterisations of Nelson Algebras

Nelson algebras arise naturally in algebraic logic as the algebraic models of Nelson’s constructive logic with strong negation. This note gives two characterisations of the variety of Nelson algebras up to term equivalence, together with a characterisation of the finite Nelson algebras up to polynomial equivalence. The results answer a question of Blok and Pigozzi and clarify some earlier work ...

Two Axiomatizations of Nelson Algebras

Nelson algebras were first studied by Rasiowa and BiałynickiBirula [1] under the name N-lattices or quasi-pseudo-Boolean algebras. Later, in investigations by Monteiro and Brignole [3, 4], and [2] the name “Nelson algebras” was adopted – which is now commonly used to show the correspondence with Nelson’s paper [14] on constructive logic with strong negation. By a Nelson algebra we mean an abstr...

A Categorical Equivalence for Product Algebras

Topological Duality for Nelson Algebras and Its Applications (abstract)

some appropriate axioms (for details see [7]). These axioms imply that the relation ≈ on A defined by: a ≈ b if and only if a → b = 1 and b → a = 1, 1)/ ≈ is a Heyting algebra. For a given Heyting algebra B there always exists a Nelson algebra A such that A h is isomorphic to B: the Fidel-Vakarelov construction of the Nelson algebra N (B) (see e.g. [8]) yields an example of such an algebra. In ...

On (Semi)Topological $BL$-algebras

In last ten years many mathematicians have studied properties of BL-algebras endowed with a topology. For example A. Di Nola and L. Leustean cite{dn} studied compact representations of BL-algebras, L. C. Ciungu cite{ciu} investigated some concepts of convergence in the class of perfect BL-algebras, J. Mi Ko and Y. C. Kim cite{jun} studied relationships between closure operators and BL-algebras,...