---
tag: EAJH1P4MK9
kind: concept
name: Filter quantifier
aliases: [filter-quantifiers, ultrafilter-quantifier, ultrafilter-quantifiers]
sources:
  - wikipedia: en:63115362@r1312275849
    locator: Filter quantifier
    note: adopted
    mention: wikipedia://en/63115362
    sections: [Summary]
same_as:
  wikidata: Q97359288
  wikipedia: Filter quantifier
inventory: [BZAEFHBFBZ]
---

## Summary

In mathematics, a filter on a set $X$ informally gives a notion of which [[subsets|0BJR9QR08E]] $A \subseteq X$ are "large". **Filter quantifiers** are a type of logical quantifier which, informally, say whether or not a statement is true for "most" elements of $X.$ Such quantifiers are often used in [[combinatorics|0JKW7W7XFR]], model theory (such as when dealing with ultraproducts), and in other fields of mathematical logic where (ultra)filters are used.