Gödel Homomorphisms as Gödel Modal Operators

We extend propositional Gödel logic by a unary modal operator, which we interpret as 5 Gödel homomorphisms, i.e. functions [0, 1] → [0, 1] that distribute over the interpretations of the 6 binary connectives of Gödel logic. We show that validity in the propositional fragment has a simple 7 superintuitionistic Hilbert-type proof system, which is not structurally complete, and that validity 8 does not change if we use the function class of continuous, strictly increasing functions. We also 9 give proof systems for restrictions to suband superdiagonal functions. 10