In mathematics, Markowsky's theorem states: every chain-complete poset is a dcpo where a poset is chain-complete if each chain in it has a least upper bound. a poset is a dcpo if each directed set in it has a least upper bound. Since a dcpo is chain-complete (as a chain is directed), the converse of the theorem is trivial.
A known proof uses Iwamura's lemma and ordinals.
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