Zorn's lemma, also known as the Kuratowski–Zorn lemma, is a proposition of set theory. It states that a partially ordered set containing upper bounds...

titled Zorns Lemma after Zorn's lemma (also known as the Kuratowski–Zorn lemma), a proposition of set theory formulated by mathematician Max Zorn in 1935...

sets amongst others. Zorn's lemma was first postulated by Kazimierz Kuratowski in 1922, and then independently by Zorn in 1935. Zorn was born in Krefeld...

lemma Sperner's lemma Urysohn's lemma Vitali covering lemma Yoneda's lemma Zorn's lemma While these results originally seemed too simple or too technical...

theory, the Teichmüller–Tukey lemma is equivalent to the axiom of choice, and therefore to the well-ordering theorem, Zorn's lemma, and the Hausdorff maximal...

example of the use of chain for referring to totally ordered subsets is Zorn's lemma which asserts that, if every chain in a partially ordered set X has an...

sets with finite complements), can be proven using from Zorn's lemma. The ultrafilter lemma is equivalent to the Boolean prime ideal theorem, with the...

set theory such as the classical theorem that the axiom of choice and Zorn's lemma are equivalent over ZF set theory. The goal of reverse mathematics, however...

field. (This order need not be uniquely determined.) The proof uses Zorn's lemma. Finite fields and more generally fields of positive characteristic cannot...

of the most common is in the proof that the axiom of choice implies Zorn's lemma. We first prove it for the case where X is chain complete and has no...