Compact propositional Gödel logics


28th International Symposium on Multiple Valued Logic. May 1998, Fukuoka, Japan. Proceedings (IEEE Computer Society Press, Los Alamitos, 1998) 108-113
(with Matthias Baaz)


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.

DOI: 10.1109/ISMVL.1998.679315


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