Abstract
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.
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Acknowledgements
We would like to thank the support of CONICET (PIP 11220170100195CO) and Departamento de Matemática (UNS) (PGI 24/L108). We would also like to thank the anonymous reviewer for his/her useful suggestions that helped us improve the article.
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Castaño, D., Cimadamore, C., Díaz Varela, J.P. et al. An Algebraic Study of S5-Modal Gödel Logic. Stud Logica 109, 937–967 (2021). https://doi.org/10.1007/s11225-020-09934-x
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DOI: https://doi.org/10.1007/s11225-020-09934-x