In this paper we continue the study of the variety \(\mathbb {MG}\) of monadic Gödel algebras. These algebras are the equivalent algebraic semantics of the S5-modal expansion of Gödel logic, which is equivalent to the one-variable monadic fragment of first-order Gödel logic. We show three families of locally finite subvarieties of \(\mathbb {MG}\) and give their equational bases. We also introduce a topological duality for monadic Gödel algebras and, as an application of this representation theorem, we characterize congruences and give characterizations of the locally finite subvarieties mentioned above by means of their dual spaces. Finally, we study some further properties of the subvariety generated by monadic Gödel chains: we present a characteristic chain for this variety, we prove that a Glivenko-type theorem holds for these algebras and we characterize free algebras over n generators.

在本文中，我们继续研究单子Gödel代数的\（\ mathbb {MG} \）。这些代数是Gödel逻辑的S5模态展开的等价代数语义，它等效于一阶Gödel逻辑的单变量单子片段。我们显示了\（\ mathbb {MG} \）的三个局部有限子变量族并给出他们的方程式基础。我们还介绍了单子Gödel代数的拓扑对偶性，并且作为该表示定理的应用，我们对等价进行了刻画，并通过它们的对偶空间对上述局部有限子变数进行了刻画。最后，我们研究了由单子Gödel链生成的子变种的其他一些特性：我们给出了该变种的特征链，证明了这些代数的Glivenko型定理成立，并且表征了n个生成器上的自由代数。