##  [Ultraproduct](/ultraproduct) 

  ##  [Ultraproduct](https://puremath.quantumdictionary.io/ultraproduct-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A structure obtained from an indexed family of structures (M_i)_{i∈I} in a common signature by taking the Cartesian product of domains and factoring by an ultrafilter U on I so that two sequences are identified when they agree on a set of indices in U; a special case is an ultrapower when all M_i are the same.