Diego N. Castaño

Free-decomposability in Varieties of Pseudocomplemented Residuated Lattices

In this paper we prove that the free pseudocomplemented residuated lattices are decomposable if and only if they are Stone, i.e., if and only if they satisfy the identity ¬x ∨ ¬¬x = 1. Some applications are given.

Indecomposability of free algebras in some subvarieties of residuated lattices and their bounded subreducts

In this paper, we show that free algebras in the variety of residuated lattices and some of its subvarieties are directly indecomposable and show, as a consequence, the direct indecomposability of free algebras for some classes of their bounded implicative subreducts.

Quasivarieties and Congruence Permutability of Łukasiewicz Implication Algebras

In this paper we study some questions concerning Łukasiewicz implication algebras. In particular, we show that every subquasivariety of Łukasiewicz implication algebras is, in fact, a variety. We also derive some characterizations of congruence permutable algebras. The starting point for these results is a representation of finite Łukasiewicz implication algebras as upwardly-closed subsets in direct products of MV-chains.

Algebraic functions in Łukasiewicz implication algebras

In this article we study algebraic functions in {→, 1}-subreducts of MV-algebras, also known as Łukasiewicz implication algebras. A function is algebraic on an algebra A if it is definable by a conjunction of equations on A. We fully characterize algebraic functions on every Łukasiewicz implication algebra belonging to a finitely generated variety. The main tool to accomplish this is a factorization result describing algebraic functions in a subproduct in terms of the algebraic functions of the factors. We prove a global representation theorem for finite Łukasiewicz implication algebras which extends a similar one already known for Tarski algebras. This result together with the knowledge of algebraic functions allowed us to give a partial description of the lattice of classes axiomatized by sentences of the form ∀∃!∧ p ≈ q within the variety generated by the 3-element chain.

Zariski‐type topology for implication algebras

In this work we provide a new topological representation for implication algebras in such a way that its one-point compactification is the topological space given in [1]. Some applications are given thereof (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Conditions for Permutability of Congruences in Implication Algebras

In this paper we give conditions on an implication algebra A so that two congruences θ1, θ2 on A permute, i.e. θ1 ∘ θ2 = θ2 ∘ θ1. We also provide simpler conditions for permutability in finite implication algebras. Finally we present some applications of these characterizations.

Gentzen-Style Sequent Calculus for Semi-intuitionistic Logic

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MV-closures of Wajsberg hoops and applications

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