I read this relevant thread on MO, but it didn't quite contain the characterization I was looking for. My question is: Suppose that we define $\mathbb Z$ to be an ordered ring with $0\neq 1$ and the property that $\mathbb Z$ is its smallest subring. Is this already enough to define the integers up to some ring-isomorphism? If someone can sketch or refer to a full proof, that would be great.
2026-04-05 00:58:50.1775350730
$\mathbb Z$ is the smallest ordered ring with $0\neq 1$?
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