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Equivalent forms of Zorn's lemma

Zorn's lemma is equivalent (in ZF) to three main results:

A well-known joke alluding to this equivalency (which may defy human intuition) is attributed to Jerry Bona:"The Axiom of Choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn's lemma?"

Zorn's lemma is also equivalent to the strong completeness theorem of first-order logic.

Moreover, Zorn's lemma (or one of its equivalent forms) implies some major results in other mathematical areas. For example,

In this sense, Zorn's lemma is a powerful tool, applicable to many areas of mathematics.