On the Fidel--Vakarelov construction for monadic Gödel algebras

[1] F. Almiñana, G. Pelaitay, Monadic k ×j-rough Heyting algebras, Archive for Mathematical Logic, 61(5-6) (2022), 611-625. https://doi.org/10.1007/s00153-021-00802-6

[2] R. Balbes, P. Dwinger, Distributive lattices, University of Missouri Press, Columbia, 1974.

[3] G. Bezhanishvili, Varieties of monadic Heyting algebras. Part I, Studia Logica, 61(3) (1998), 367-402. https: //doi.org/10.1023/A:1005073905902

[4] I. Calomino, G. Pelaitay, L. F. Valverde, Heyting algebras with Kalman-Galois connections, Studia Logica, (2025), 1-37. https://doi.org/10.1007/s11225-025-10179-9

[5] D. Castaño, C. Cimadamore, J. P. Díaz Varela, L. Rueda, Monadic BL-algebras: The equivalent algebraic semantics of Hájek’s monadic fuzzy logic, Fuzzy Sets and Systems, 320 (2017), 40-59. https://doi.org/10.1016/j.fss. 2016.12.007

[6] J. L. Castiglioni, S. Celani, H. J. San Martín, Kleene algebras with implication, Algebra Universalis, 77 (2017), 375-393. https://doi.org/10.1007/s00012-017-0433-4

[7] I. Chajda, M. Kolařík, Monadic basic algebras, Acta Universitatis Palackianae Olomucensis. Facultas Re rum Naturalium. Mathematica, 47(1) (2008), 27-36. https://dml.cz/bitstream/handle/10338.dmlcz/133403/ ActaOlom_47-2008-1_3.pdf

[8] I. Chajda, H. Länger, Quantifiers on lattices with an antitone involution, Demonstratio Mathematica, 42(2) (2009), 241-246. https://doi.org/10.1515/dema-2009-0203

[9] R. Cignoli, The class of Kleene algebras satisfying an interpolation property and Nelson algebras, Algebra Universalis, 23 (1986), 262-292. https://doi.org/10.1007/BF01230621

[10] A. Di Nola, R. Grigolia, On monadic MV-algebras, Annals of Pure and Applied Logic, 128(1-3) (2004), 125-139. https://doi.org/10.1016/j.apal.2003.11.031

[11] A. Di Nola, R. Grigolia, G. Lenzi, Topological spaces of monadic MV-algebras, Soft Computing, 23(2) (2019), 375-381. https://doi.org/10.1007/s00500-018-3166-1

[12] F. Esteva, A. Figallo-Orellano, T. Flaminio, L. Godo, Logics of formal inconsistency based on distributive involutive residuated lattices, Journal of Logic and Computation, 31(5) (2021), 1226-1265. https://doi.org/10.1093/ logcom/exab029

[13] F. Esteva, A. Figallo-Orellano, T. Flaminio, L. Godo, Some categorical equivalences for Nelson algebras with consistency operators, in: Joint Proceedings of IFSA–EUSFLAT–AGOP 2021, Atlantis Studies in Uncertainty Modelling, 3 (2021), 420-426. https://doi.org/10.2991/asum.k.210827.056

[14] M. M. Fidel, An algebraic study of a propositional system of Nelson, in: A. I. Arruda, N. C. A. da Costa and R. Chuaqui (eds.), Mathematical Logic: Proceedings of the First Brazilian Conference, Lectures in Pure and Applied Mathematics, 39, Marcel Dekker, New York, (1978), 99-117.

[15] C. Gallardo, A. Ziliani, A generalization of monadic n-valued Lukasiewicz algebras, Studia Logica, 110 (2022), 457-478. https://doi.org/10.1007/s11225-021-09968-9

[16] P. R. Halmos, Algebraic logic, Chelsea, New York, 1962. https://doi.org/10.2307/2964557

[17] J. A. Kalman, Lattices with involution, Transactions of the American Mathematical Society, 87(2) (1958), 485-491. https://doi.org/10.2307/1993112

[18] A. Monteiro, Construction des algèbres de Nelson finies, Bulletin de l’Academie Polonaise des Sciences, Sér. Sci. Math. Astron. Phys., 11 (1963), 359-362.

[19] A. Monteiro, Les N-lattices linéaires, Informe Técnico Interno, 43 (1978), 2055-2060.

[20] A. Monteiro, L. Monteiro, Axiomes indépendants pour les algébres de Nelson, de Lukasiewicz trivalentes, de De Morgan et de Kleene, Notas de Lógica Matemática 40, Universidad Nacional del Sur, Bahía Blanca, 1996. https: //hdl.handle.net/20.500.14330/PER01000020678

[21] A. Monteiro, O. Varsavsky, Algebras de Heyting monádicas, Actas de las X Jornadas de la Unión Matemática Argentina, (1957), 52-62.

[22] D. Nelson, Constructible falsity, The Journal of Symbolic Logic, 14(1) (1949), 16-26. https://doi.org/10.2307/ 2268973

[23] H. Rasiowa, N-lattices and constructive logic with strong negation, Fundamenta Mathematicae, 46(1) (1958), 61-80. https://doi.org/10.4064/fm-46-1-61-80

[24] U. Rivieccio, Implicative twist-structures, Algebra Universalis, 71(2) (2014), 155-186. https://doi.org/10.1007/ s00012-014-0272-5

[25] A. Sendlewski, Nelson algebras through Heyting ones I, Studia Logica, 49(1) (1990), 105-126. https://doi.org/ 10.1007/BF00401557

[26] D. Vakarelov, Notes on N-lattices and constructive logic with strong negation, Studia Logica, 36(1-2) (1977), 109-125. https://doi.org/10.1007/BF02121118

[27] J. T. Wang, Y. H. She, P. F. He, N. N. Ma, On categorical equivalence of weak monadic residuated distributive lattices and weak monadic c-differential residuated distributive lattices, Studia Logica, 111 (2023), 361-390. https: //doi.org/10.1007/s11225-022-10026-1