Tarski's undefinability theorem

Tarski's undefinability theorem, stated and proved by Alfred Tarski in 1933, is an important limitative result in mathematical logic, the foundations of mathematics, and in formal semantics. Informally, the theorem states that "arithmetical truth cannot be defined in arithmetic".

The theorem applies more generally to any sufficiently strong formal system, showing that truth in the standard model of the system cannot be defined within the system.