Zorn's lemma

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A proposition in set theory equivalent to the axiom of choice. Call a set A a chain if for any two members B and C, either B is a subset of C or C is a subset of B. Now consider a set D with the properties that for every chain E that is a subset of D, the union of E is a member of D. The lemma states that D contains a member that is maximal, i.e. which is not a subset of any other set in D.

Subjects: Philosophy.

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