= Solution
For each positive integer $n$, the finite ordered interval $[-n,n]\cap\mathbb Z$ has a greatest and a least element, and these intervals form a chain of <substructures>. Their union is $\mathbb Z$, which has neither. An <inductive first-order theory> must be preserved by such unions, as proved above. \b[The theory with both endpoints cannot be axiomatized inductively], even though it has an ordinary first-order axiomatization with existential–universal endpoint sentences.
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