Gödel numbering

In mathematical logic, a Gödel numbering is a function that assigns to each symbol and well-formed formula of some formal language a unique natural number, called its Gödel number.

Description

The concept was used by Kurt Gödel for the proof of his incompleteness theorems. (Gödel 1931)

A Gödel numbering can be interpreted as an encoding in which a number is assigned to each symbol of a mathematical notation, after which a sequence of natural numbers can then represent a sequence of symbols. These sequences of natural numbers can again be represented by single natural numbers, facilitating their manipulation in formal theories of arithmetic.

Mathematical objects

Since the publishing of Gödel's paper in 1931, the term "Gödel numbering" or "Gödel code" has been used to refer to more general assignments of natural numbers to mathematical objects.

See also

• Encoding
• Formal language
• Function (mathematics)
• Incompleteness theorems
• Kurt Gödel
• Mathematical logic
• Mathematical notation
• Mathematical object
• Natural number
• Symbol
• Well-formed formula

External links

• Gödel numbering @ Wikipedia