The ultraproduct is a mathematical construction that appears mainly in abstract algebra and in model theory, a branch of mathematical logic. An ultraproduct is a quotient of the direct product of a family of structures. All factors need to have the same signature. The ultrapower is the special case of this construction in which all factors are equ...
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http://en.wikipedia.org/wiki/Ultraproduct
(from the article `metalogic`) A particularly useful tool for obtaining new models from the given models of a theory is the construction of a special combination called the ... An ultrafilter on a nonempty set is defined as a set of subsets of such that (1) the empty set does not belong to ,[2 related articles]
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http://www.britannica.com/eb/a-z/u/4
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