Compact propositional Gödel logics

In Baaz Matthias (ed.), 28th IEEE International Symposium on Multiple-Valued Logic, 1998. Proceedings. IEEE Press. pp. 108-113 (1998)
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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.

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Richard Zach
University of Calgary


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