##  [Ultrafilter Lemma](/ultrafilter-lemma) 

  ##  [Ultrafilter Lemma](https://mathlogic.quantumdictionary.io/ultrafilter-lemma-0) 

  

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**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The assertion that every proper filter on a Boolean algebra or on the power set of a set can be extended to an ultrafilter, equivalently that every family of sets with the finite intersection property is contained in an ultrafilter; commonly used to construct ultraproducts and nonprincipal ultrafilters.