RhymeZone: ultrafilter definitions

Definitions of ultrafilter:

noun: A device that performs ultrafiltration.
noun: (mathematics, of a set, whose subsets are partially ordered by inclusion) A proper filter which has a law of dichotomy for complements.
noun: (mathematics, order theory) A filter (subset of a poset) that is maximal as a set with respect to the definition of proper filter.
verb: (transitive) To filter by ultrafiltration.

(Definitions from Wiktionary)