A note on 3 × 3-valued lukasiewicz algebras with negation
Bulletin of the Section of Logic, ISSN: 0138-0680, Vol: 50, Issue: 3, Page: 289-298
2021
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Article Description
In 2004, C. Sanza, with the purpose of legitimizing the study of n × m-valued Łukasiewicz algebras with negation (or NSn×m-algebras) introduced 3×3-valued Łukasiewicz algebras with negation. Despite the various results obtained about NSn×m-algebras, the structure of the free algebras for this variety has not been determined yet. She only obtained a bound for their cardinal number with a finite number of free generators. In this note we describe the structure of the free finitely generated NS3×3-algebras and we determine a formula to calculate its cardinal number in terms of the number of free generators. Moreover, we obtain the lattice Λ(NS3×3) of all subvarieties of NS3×3 and we show that the varieties of Boolean algebras, three-valued Łukasiewicz algebras and four-valued Łukasiewicz algebras are proper subvarieties of NS3×3.
Bibliographic Details
Uniwersytet Lodzki (University of Lodz)
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