Home > Diagonalization lemma

In mathematical logic, the diagonalization lemma states that for any well formed formula

with a free variable x, there is a sentence ψ such that

where [ψ] is the Gödel number for ψ.

Gödel's first incompleteness theorem can be proved via the diagonalization lemma.

It takes its name from Cantor's diagonal argument to prove that the real numbers are uncountable.

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DiagonalizationThe term diagonalization is used in two different senses in mathematics: The process of finding a diagonal matrix similar to a given square matrix or representing a given linear map. See diagonalizable matrix for more. A certain proof technique used to sh

Diagonalization lemmaIn mathematical logic, the diagonalization lemma states that for any well formed formula with a free variable x there is a sentence ψ such that : where [ψ] is the Godel number for ψ. Godel's first incompleteness theorem can be proved via the d

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