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Q: Countable ordinals are embeddable in the rationals $\Bbb Q$ -- proofs and their use of AC

Lord_FarinYesterday, Asaf Karagila's answer to my question sparked an extensive discussion on ways of proving that all countable ordinals are embeddable in $\Bbb Q$, and whether particular solutions to this use the Axiom of Choice. Since the arguments used to prove this can be shady on their use of Choice...

set-theory order-theory axiom-of-choice ordinals

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