Gödel-Dummett logic is the logic obtained if we extend intuitionistic propositional logic by the axiom
[Dummett 1959] showed that is true in Gödel-Dummett logic if and only if it is valid in all Heyting algebras that are finite chains.
Federico Aschieri, Agata Ciabattoni, and Francesco A. Genco. 2017. Gödel logic: from natural deduction to parallel computation. In Proceedings of the 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS '17). IEEE Press, Article 16, 1–12.
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