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Talking about suborders of $\mathbb{Q}$ explicitly makes things a bit harder to think about than is necessary, in my opinion. Really we should be talking about general computable (or rather, c.e.) linear orders - the point is that $\mathbb{Q}$ is "big enough" that we can WLOG construe these as suborders of $\mathbb{Q}$ for concreteness. This does ...


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