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- Again, to specify a structure you need to specify not just the domain of discourse, but the underlying first-order theory being interpreted. Based on the context it seems like the theory of real-closed fields, with the domain of discourse being the standard model of the real numbers in ZFC. Fine, but again this should not be implicit based on context for an introductory article. (en)
- This seems to be conflating syntax and semantics, at least to the extent that the first-order theory being modelled isn't explictly stated. Presumably the author had in mind Peano arithmetic, and is considering the standard model in ZFC as the structure, but again it would be a lot more useful for novices if important subtleties like that aren't swept under the rug, because they most likely lack the ability yet to correctly infer the syntax and semantics from context. (en)
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