- Tytuł:
- A Note on 3×3-valued Łukasiewicz Algebras with Negation
- Autorzy:
-
Gallardo, Carlos
Ziliani, Alicia - Powiązania:
- https://bibliotekanauki.pl/articles/2033855.pdf
- Data publikacji:
- 2021-05-27
- Wydawca:
- Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
- Tematy:
-
\(n\)-valued Łukasiewicz-Moisil algebras
\(n \times m\)-valued Łukasiewicz algebras with negation
free algebras
lattice of subvarieties - Opis:
- In 2004, C. Sanza, with the purpose of legitimizing the study of \(n\times m\)-valued Łukasiewicz algebras with negation (or \(\mathbf{NS}_{n\times m}\)-algebras) introduced \(3 \times 3\)-valued Łukasiewicz algebras with negation. Despite the various results obtained about \(\mathbf{NS}_{n\times m}\)-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 \(NS_{3 \times 3}\)-algebras and we determine a formula to calculate its cardinal number in terms of the number of free generators. Moreover, we obtain the lattice \(\Lambda(\mathbf{NS}_{3\times 3})\) of all subvarieties of \(\mathbf{NS}_{3\times 3}\) and we show that the varieties of Boolean algebras, three-valued Łukasiewicz algebras and four-valued Łukasiewicz algebras are proper subvarieties of \(\mathbf{NS}_{3\times 3}\).
- Źródło:
-
Bulletin of the Section of Logic; 2021, 50, 3; 289-298
0138-0680
2449-836X - Pojawia się w:
- Bulletin of the Section of Logic
- Dostawca treści:
- Biblioteka Nauki
Artykuł