Characterization of the axiomatizable prenex fragments of first-order Gödel logics

Baaz, Matthias, Norbert Preining, and Richard Zach. 2003. “Characterization of the Axiomatizable Prenex Fragments of First-Order Gödel Logics.” In 33rd International Symposium on Multiple-Valued Logic. May 2003, Tokyo, Japan. Proceedings, 175–80. Los Alamitos: IEEE Press.

The prenex fragments of first-order infinite-valued Gödel logics are classified. It is shown that the prenex Gödel logics characterized by finite and by uncountable subsets of [0, 1] are axiomatizable, and that the prenex fragments of all countably infinite Gödel logics are not axiomatizable.

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