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Topic: Why don't texts give a stronger version of Zorn's lemma?
Replies: 6   Last Post: Nov 20, 2013 12:09 PM

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Registered: 7/12/10
Why don't texts give a stronger version of Zorn's lemma?
Posted: Nov 19, 2013 6:52 PM
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Why isn't the standard version of Zorn's lemma as follows? :
Let X be a partially ordered set such that every well-ordered subset has an upper bound. Then X has a maximal element.

It's stronger than the standard one, and no more difficult to prove from AC.

Paul Epstein

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