A categorial equivalence for semi-Nelson algebras

Soft Computing - Tập 25 - Trang 13813-13821 - 2021
Juan Manuel Cornejo1, Andrés Gallardo1, Ignacio Viglizzo1
1Instituto de Matemática (INMABB), Departamento de Matemática, Universidad Nacional del Sur (UNS) - CONICET, Buenos Aires, Argentina

Tóm tắt

We present a category equivalent to that of semi-Nelson algebras. The objects in this category are pairs consisting of a semi-Heyting algebra and one of its filters. The filters must contain all the dense elements of the semi-Heyting algebra and satisfy an additional technical condition. We also show that the category of dually hemimorphic semi-Nelson algebras is equivalent to that of dually hemimorphic semi-Heyting algebras.

Tài liệu tham khảo

Abad M, Cornejo JM, Varela JPD (2013) Semi-Heyting algebras term-equivalent to Godel algebras. Order, 30(2): 625-642

Balbes R, Dwinger P (1974) Distributive lattices. University of Missouri Press, Columbia, Mo

Cornejo JM, San Martín HJ (2018) A categorical equivalence between semi-Heyting algebras and centered semi-Nelson algebras. Logic J IGPL 26(4):408–428

Cornejo JM, San Martín HJ (2020) Dually hemimorphic semi-Nelson algebras. Log J IGPL 28(3):316–334

Cornejo JM, Viglizzo I (2018) Semi-Nelson algebras. Order 35(1):23–45

Kalman JA (1958) Lattices with involution. Trans Amer Math Soc 87:485–491

Monteiro A, Monteiro L (1996) Axiomes indépendants pour les algèbres de Nelson, de Łukasiewicz trivalentes, de De Morgan et de Kleene. In Unpublished papers, I, Notas Lógica Mat 40:13

Monteiro A, Monteiro L (1996) Axiomes indépendants pour les algèbres de Nelson, de Lukasiewicz trivalentes, de De Morgan et de Kleene. In Unpublished papers I, Notas Lógica Mat. 40:13

Sankappanavar HP (1985) Semi-Heyting algebras. Amer Math Soc Abstracts, 13

Sankappanavar HP (2008) Semi-Heyting algebras: an abstraction from Heyting algebras. In Proceedings of the 9th “Dr. Antonio A. R. Monteiro” Congress (Spanish), Actas Congr. “Dr. Antonio A. R. Monteiro”, pages 33–66, Bahía Blanca, 2008. Univ Nac del Sur

Sankappanavar HP (2011) Expansions of semi-Heyting algebras I: discriminator varieties. Studia Logica 98(1–2):27–81

Sendlewski A (1984) Some investigations of varieties of \({\cal{N}}\)-lattices. Studia Logica 43(3):257–280

Sendlewski A (1990) Nelson algebras through Heyting ones. I Studia Logica 49(1):105–126

Vakarelov D (1977) Notes on \({\cal{N}}\)-lattices and constructive logic with strong negation. Studia Logica 36(1–2):109–125

Viglizzo I (1999) Álgebras de Nelson. Instituto de Matemática de Bahía Blanca, Universidad Nacional del Sur, 1999. Magister dissertation in Mathematics, Universidad Nacional del Sur, Bahía Blanca, available at https://sites.google.com/site/viglizzo/viglizzo99nelson

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Soft Computing

Tập 25

13813-13821

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