##  [Algebraic Closure (Model-Theoretic)](/algebraic-closure-model-theoretic) 

  ##  [Algebraic Closure (Model-Theoretic)](https://algebra.quantumdictionary.io/algebraic-closure-model-theoretic-0) 

  

 [![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

In a given first-order structure or model M and for a parameter set A ⊆ M, the model-theoretic algebraic closure acl(A) is the set of all elements of M that satisfy some formula with parameters from A that has only finitely many solutions in M. It is a closure operator capturing finite definability over A in the model-theoretic sense.