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** Zorn's lemma: Every non-empty partially ordered set in which every chain ( i. e. totally ordered subset ) has an upper bound contains at least one maximal element.
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** and lemma
** Tukey's lemma: Every non-empty collection of finite character has a maximal element with respect to inclusion.
** and Every
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** and non-empty
** and partially
** Hausdorff maximal principle: In any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset.
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