📜 Theorem, law or theory

Kuratowski–Zorn lemma

Lema de Kuratowski-Zorn

Date
1922 · confidence high
Place
Warsaw, Poland
Credited to
Kazimierz Kuratowski, rediscovered by Max Zorn in 1935
Field
Knowledge & symbols

⚠️ Disputed: the sources disagree.

What was discovered

Kuratowski proved in 1922 a version close to the modern one of the principle stating that every ordered set in which every chain has an upper bound has a maximal element; Max Zorn independently reached the same result in 1935 and proposed it as an axiom alternative to well-ordering.

The common name, "Zorn's lemma," comes from John Tukey popularizing it that way in 1940; in Poland and Russia it is still called the "Kuratowski–Zorn lemma" in recognition of Kuratowski's priority.

What it led to

  • Routine use of the lemma as a tractable equivalent of the axiom of choice
  • Existence proofs for bases, maximal ideals and other structures in algebra
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Sources✓ verified 2026-09-28