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About: Reduced product     Goto   Sponge   NotDistinct   Permalink

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In model theory, a branch of mathematical logic, and in algebra, the reduced product is a construction that generalizes both direct product and ultraproduct. Let {Si | i ∈ I} be a family of structures of the same signature σ indexed by a set I, and let U be a filter on I. The domain of the reduced product is the quotient of the Cartesian product by a certain equivalence relation ~: two elements (ai) and (bi) of the Cartesian product are equivalent if Operations from σ are interpreted on the reduced product by applying the operation pointwise. Relations are interpreted by