##  [Elimination of Imaginaries](/index.php/elimination-imaginaries) 

  ##  [Elimination of Imaginaries](https://mathlogic.quantumdictionary.io/elimination-imaginaries-0) 

  

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

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A property of a theory that every definable equivalence class (an 'imaginary') can be coded by a tuple of real elements (elements of the home sorts), so that every imaginary has a canonical parameter in the real sorts and no extra imaginary sorts are needed.

 

 

 

 

 





 

 



 ##  [Elimination of Imaginaries](https://algebra.quantumdictionary.io/elimination-imaginaries-1) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/index.php/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A property of a theory saying that every definable set (with parameters) admits a canonical parameter (an 'imaginary' element) in the home sorts or in a definable expansion, so definable quotients are represented by real elements or named sorts.