##  [Elementary Diagram](/elementary-diagram) 

  ##  [Elementary Diagram](https://mathlogic.quantumdictionary.io/elementary-diagram-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

For a structure M in a language L, the elementary diagram is the set of all first-order L(M)-sentences (where L(M) is L expanded with a constant for each element of M) that are true in the expanded structure; it records every first-order fact about named elements of M.

 

 

 

 

 





 

 



 ##  [Elementary Diagram](https://algebra.quantumdictionary.io/elementary-diagram-1) 

  

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

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

Given a structure A, the elementary diagram Diag(A) is the set of all atomic and negated atomic sentences in the language expanded by naming each element a ∈ A with a new constant symbol c_a, that are true in A. It records complete atomic-level information about A with constants.