A note on Sugihara algebras.

Josep M. Font; Gonzalo Rodríguez Pérez

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In this paper, the variety of closure n-valued Łukasiewicz algebras, that is, Łukasiewicz algebras of order n endowed with a closure operator, is investigated. The lattice of subvarieties in the particular case in which the open elements form a three-valued Heyting algebra is obtained.

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Celani, Sergio Arturo (2006)

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Modal Pseudocomplemented De Morgan Algebras

Aldo V. Figallo, Nora Oliva, Alicia Ziliani (2014)

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Modal pseudocomplemented De Morgan algebras (or $m p M$ -algebras for short) are investigated in this paper. This new equational class of algebras was introduced by A. V. Figallo and P. Landini ([Figallo, A. V., Landini, P.: Notes on $4$ -valued modal algebras Preprints del Instituto de Ciencias Básicas, Univ. Nac. de San Juan 1 (1990), 28–37.]) and they constitute a proper subvariety of the variety of all pseudocomplemented De Morgan algebras satisfying $x \land {(\sim x)}^{*} = {(\sim (x \land {(\sim x)}^{*}))}^{*}$ . Firstly, a topological duality for these...

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The main goal of this paper is to investigate very true MTL-algebras and prove the completeness of the very true MTL-logic. In this paper, the concept of very true operators on MTL-algebras is introduced and some related properties are investigated. Also, conditions for an MTL-algebra to be an MV-algebra and a Gödel algebra are given via this operator. Moreover, very true filters on very true MTL-algebras are studied. In particular, subdirectly irreducible very true MTL-algebras are...

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We obtain a simple construction for particular subclasses of several varieties of lattice expansions. The construction allows a unified approach to the characterization of the subdirectly irreducible algebras