Definitions for ultrafilterˌʌl trəˈfɪl tər
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A filter that is maximal as a set with respect to the definition of .
In the mathematical field of set theory, an ultrafilter on a set X is a collection of subsets of X that is a filter, that cannot be enlarged. An ultrafilter may be considered as a finitely additive measure. Then every subset of X is either considered "almost everything" or "almost nothing". If A is a subset of X, then either A or X \ A is an element of the ultrafilter. The concept can be generalized to Boolean algebras or even to general partial orders, and has many applications in set theory, model theory, and topology.
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