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Erratum to “The Ricean objection: An analogue of Rice’s theorem for first-order theories”. (English) Zbl 1181.03046
In [Log. J. IGPL 16, No. 6, 585–590 (2008; Zbl 1159.03028)] the authors had stated and proved a result they called “Rice’s theorem for logic”, claiming that “If Prop is a nontrivial property of first-order theories, then Prop is undecidable.” It turns out that there is a flaw in the proof, and that the result is false. The authors provide a concrete example of a non-trivial decidable property for any consistent decidable theory, to show that their earlier result is false. “Rice’s theorem for logic” can be saved if one replaces “first-order theories” in its statement with “Robinson’s \(Q\)”.
MSC:
03D35 Undecidability and degrees of sets of sentences
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