##  [Diagonal Lemma](/diagonal-lemma) 

  ##  [Diagonal Lemma](https://mathlogic.quantumdictionary.io/diagonal-lemma-0) 

  

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- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A syntactic lemma in formal arithmetic that guarantees for any formula φ(x) the existence of a sentence ψ such that the theory proves ψ ↔ φ(⌜ψ⌝), i.e., a sentence that asserts a property about its own Gödel number.