Goodstein's theorem
Teorema de Goodstein
- Date
- 1944 · confidence high
- Place
- Reading, England, United Kingdom
- Credited to
- Reuben Goodstein
- Field
- Knowledge & symbols
What was discovered
Number-theory theorem stating that every Goodstein sequence eventually terminates at zero, proved by Reuben Goodstein and notable for being unprovable within Peano arithmetic.
What it led to
- Kirby and Paris's 1982 proof of its independence from Peano arithmetic
- Prominent example of a true but unprovable statement in formal systems
- Contributions to mathematical logic and proof theory
- Teaching example of the limits of Peano arithmetic