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On the Fidel--Vakarelov construction for monadic G\"odel algebras | ||
| Iranian Journal of Fuzzy Systems | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 25 شهریور 1405 اصل مقاله (384.39 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2026.55173.9787 | ||
| نویسندگان | ||
| María Valentina Alonso؛ Gustavo Pelaitay* | ||
| Instituto de Ciencias Básicas, Universidad Nacional de San Juan and CONICET | ||
| چکیده | ||
| The classical Fidel--Vakarelov construction connects Heyting algebras with centered Nelson algebras through a twist representation. We investigate whether this construction is compatible with monadic operators. We introduce monadic centered prelinear Nelson algebras and prove that the Fidel--Vakarelov construction yields a categorical equivalence between monadic G\"odel algebras and this new class. We also show, by a finite counterexample, why the additional monadic G\"odel equation is necessary, and we establish an order isomorphism between the corresponding congruence lattices. | ||
| کلیدواژهها | ||
| Heyting algebras؛ Nelson algebras؛ monadic G\"odel algebras؛ twist structures | ||
| مراجع | ||
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