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