Baaz, Matthias, and Richard Zach. 1998. “Compact Propositional Gödel Logics.” In 28th International Symposium on Multiple-Valued Logic. May 1998, Fukuoka, Japan. Proceedings, 108–13. Los Alamitos: IEEE Press. https://doi.org/10.1109/ISMVL.1998.679315.

Entailment in propositional Gödel logics can be defined in a natural way. While all infinite sets of truth values yield the same sets of tautologies, the entailment relations differ. It is shown that there is a rich structure of infinite-valued Gödel logics, only one of which is compact. It is also shown that the compact infinite-valued Gödel logic is the only one which interpolates, and the only one with an r.e. entailment relation.