##  [Conservative Extension](/conservative-extension) 

  ##  [Conservative Extension](https://mathlogic.quantumdictionary.io/conservative-extension-0) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An extension T' of a theory T is conservative if T' proves no new sentences in the language of T beyond those provable in T itself; equivalently, every sentence in the original language provable in the extension was already provable in the base theory.