Editing Zorn's lemma (section)

==History==
The [[Hausdorff maximal principle]] is an early statement similar to Zorn's lemma.

[[Kazimierz Kuratowski]] proved in 1922<ref>{{cite journal |first=Casimir |last=Kuratowski |title=Une méthode d'élimination des nombres transfinis des raisonnements mathématiques |trans-title=A method of disposing of transfinite numbers of mathematical reasoning |journal=[[Fundamenta Mathematicae]] |volume=3 |year=1922 |pages=76–108 |doi=10.4064/fm-3-1-76-108 |url=http://matwbn.icm.edu.pl/ksiazki/fm/fm3/fm3114.pdf |access-date=2013-04-24 |language=fr|doi-access=free }}</ref> a version of the lemma close to its modern formulation (it applies to sets ordered by inclusion and closed under unions of well-ordered chains). Essentially the same formulation (weakened by using arbitrary chains, not just well-ordered) was independently given by [[Max August Zorn|Max Zorn]] in 1935,<ref>{{cite journal |first=Max |last=Zorn |title=A remark on method in transfinite algebra |journal=Bulletin of the American Mathematical Society |volume=41 |year=1935 |issue=10 |pages=667–670 |doi=10.1090/S0002-9904-1935-06166-X |doi-access=free }}</ref> who proposed it as a new [[axiom]] of set theory replacing the well-ordering theorem, exhibited some of its applications in algebra, and promised to show its equivalence with the axiom of choice in another paper, which never appeared.

The name "Zorn's lemma" appears to be due to [[John Tukey]], who used it in his book ''Convergence and Uniformity in Topology'' in 1940. [[Nicolas Bourbaki|Bourbaki]]'s ''Théorie des Ensembles'' of 1939 refers to a similar maximal principle as "le théorème de Zorn".<ref>{{harvnb|Campbell|1978|p=82}}.</ref> The name "[[:pl:lemat Kuratowskiego-Zorna|Kuratowski–Zorn lemma]]" prevails in Poland and Russia.

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