On the Fidel--Vakarelov construction for monadic Gödel algebras

Document Type : Original Manuscript

Authors

Instituto de Ciencias Básicas, Universidad Nacional de San Juan and CONICET

Abstract

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.

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References

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Iranian Journal of Fuzzy Systems
Volume 23, Issue 6
November and December 2026
Pages 39-50

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