Markowsky or Cohn?

I have already mentioned Markowsky’s Theorem (1976): every chain-complete poset is a dcpo.  This is a non-trivial theorem, and I’ve given you a proof of it based on Iwamura’s Lemma and ordinals in a previous post.  Maurice Pouzet recently pointed me to P. M. Cohn’s book Universal algebra (1965), where you can find the same theorem already!  Cohn’s proof is very different and does not rely on Iwamura’s Lemma.  Let me describe it in the full post.