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A non-arithmetical Gödel logic. (English) Zbl 1086.03018
The paper focuses on two special cases of Gödel logic, namely the logics \(G_{\downarrow}\), which is based on the set of truth values \(V_{\downarrow}= \{\frac{a}{n}\mid n= 1, 2, \ldots\}\cup \{0\}\), and \(G_{\uparrow}\), based on \(V_{\uparrow}= \{\frac{n}{n+1}\mid n= 0, 1, 2, \ldots\}\cup \{1\}\). It is shown that the set of tautologies as well as the set of satisfiable formulas of \(G_{\downarrow}\) are non-arithmetical. On the other hand, the set of tautologies of \(G_{\uparrow}\) is proved to be \(\Pi_2\)-complete.

MSC:
03B52 Fuzzy logic; logic of vagueness
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