Axiom of choice and Zermelo-Fraenkel set theory
Axioma de elección y axiomática de Zermelo-Fraenkel
- Date
- 1904-1908 · confidence high
- Place
- Göttingen, Germany
- Credited to
- Ernst Zermelo (1904, 1908); Abraham Fraenkel and Thoralf Skolem (1922)
- People
- 👤 Ernst Zermelo1871–1953
- Field
- Knowledge & symbols
What was discovered
The explicit formulation of the axiom of choice to prove the well-ordering theorem, and the first axiomatisation of set theory, which avoids the paradoxes and today serves as the standard foundation (ZFC) of mathematics.
The axiom of choice was highly controversial (Borel, Lebesgue, Baire) for its non-constructive consequences.
What it led to
- ZFC foundations
- Zorn's lemma
- the Banach-Tarski paradox
- independence results (Gödel, Cohen)