Diagonal lemma
Statement in mathematical logic / From Wikipedia, the free encyclopedia
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This article is about a concept in mathematical logic. It is named in reference to Cantor's diagonal argument in set and number theory. See diagonalization (disambiguation) for several unrelated uses of the term in mathematics.
In mathematical logic, the diagonal lemma (also known as diagonalization lemma, self-reference lemma[1] or fixed point theorem) establishes the existence of self-referential sentences in certain formal theories of the natural numbers—specifically those theories that are strong enough to represent all computable functions. The sentences whose existence is secured by the diagonal lemma can then, in turn, be used to prove fundamental limitative results such as Gödel's incompleteness theorems and Tarski's undefinability theorem.[2]