I heard that Zorn's lemma is equivalent to Tukey's lemma. Now I've proved that Zorn's lemma implies that Tukey's lemma but I cannot prove that Tukey's lemma implies Zorn's lemma. How to show this?
How to show Tukey's Lemma proves Zorn's lemma?
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set-theory
axiom-of-choice
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0This question is somewhat related: [Tukey's lemma by axiom of choice](http://math.stackexchange.com/questions/135655/tukeys-lemma-by-axiom-of-choice). – 2012-05-31