Talk:Completeness (order theory)
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[edit] Question about A poset is chain-complete iff it is a dcpo.
The following equivalence requires the Axiom of Choice:
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- A poset is chain-complete iff it is a dcpo.
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- Can anybody give a proof of this proposition?
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- A poset is chain-complete iff it is a dcpo.
(this is an anon question I moved from the article page) Oleg Alexandrov 17:32, 22 Apr 2005 (UTC)
Chain-completeness is a stronger notion than omega-completeness, contrary to the definition given in the article. Omega-completeness says that every chain of order type omega has a least upper bound, whereas chain-completeness says that every totally ordered set (regardless of order type) has a least upper bound. (WilliamDClinger (talk) 19:52, 4 June 2008 (UTC))
