Peano axioms
Axiomas de Peano para los números naturales
- Date
- 1889 · confidence high
- Place
- Turin, Italy
- Credited to
- Giuseppe Peano (Arithmetices principia); earlier formulation by Dedekind (1888)
- People
- 👤 Giuseppe Peano1858–1932
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What was discovered
A characterisation of the natural numbers by means of zero, successor and induction, in symbolic notation. It is the reference formal system on which Gödel proved incompleteness.
Dedekind published an equivalent characterisation a year earlier; Peano acknowledged the debt.
What it led to
- the foundations of arithmetic
- the incompleteness theorems
- recursion theory
- formal verification
Built on
- Dedekind (Was sind und was sollen die Zahlen)
- Grassmann