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Definition: A formal logic system is decidable – if there is an algorithm that can determine if any given sentence is a theorem (or not).

Based on this definition, I am not sure how to move to prove that, "any first-order logics with equality and a relation/functional symbol of arity more than 1." Example also can help if you can write one.

Thanks.

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  • $\begingroup$ Example: How about the first-order axioms of Peano arithmetic? $\endgroup$
    – ShyPerson
    Aug 30, 2023 at 20:51

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