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This Question has an answer which is the only source that I can find about how $\mathbb{R}/\mathbb{Q}$ cannot be linearly ordered. I couldn't manage to open either of the source links provided in the answer. Could someone please explain why $\mathbb{R}/\mathbb{Q}$ can only be linearly ordered with the Axiom of Choice in a way that is understandable to a graduate with set theory knowledge?

Adam
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  • The source is Sur une proposition qui entraîne l'existence des ensembles non mesurables by Sierpiński. There is a link to it here, of course in French – Jakobian Jun 08 '24 at 09:50
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    Note that the answer doesn't say that in the absence of AC you can never linearly order $\mathbb{R}/\mathbb{Q}$, but that its consistent with ZF that you can't linearly order $\mathbb{R}/\mathbb{Q}$ – Jakobian Jun 08 '24 at 09:52
  • See this answer – Holo Jun 08 '24 at 11:43

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