In mathematics, especially in category theory and algebra, the term "reduced product" can refer to various concepts depending on the context.
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Given nonempty first-order structures and a proper filter on a set , a reduced product identifies product functions when . Operations are interpreted coordinatewise, and relations hold when their coordinate truth sets belong to . For an ultrafilter this is an ultraproduct. Primitive positive formulas transfer through an arbitrary proper filter, whereas logical disjunction and logical negation can fail to transfer.