##  [Ultraproduct Construction](/ultraproduct-construction) 

  ##  [Ultraproduct Construction](https://mathlogic.quantumdictionary.io/ultraproduct-construction-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

A model-theoretic construction that forms a new structure by taking the Cartesian product of a family of structures and quotienting by an ultrafilter, used to transfer properties and produce limit-like models.

 

 

 

 

 





 

 



 ##  [Ultraproduct Construction](https://algebra.quantumdictionary.io/ultraproduct-construction-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

A model-theoretic construction that forms a new structure from a family (A_i)_{i∈I} of structures of the same signature and an ultrafilter U on I by taking the Cartesian product modulo the equivalence relation that identifies two sequences when they agree on a set in U; first-order properties satisfied on a U-large set transfer to the ultraproduct.