Filter quantifier

Summary

In mathematics, a filter on a set $X$ informally gives a notion of which subsets $A \subseteq X$ 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, model theory (such as when dealing with ultraproducts), and in other fields of mathematical logic where (ultra)filters are used.