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Reduct
In universal algebra and in model theory, a reduct of an algebraic structure is obtained by omitting some of the operations and relations of that structure. The converse of "reduct" is "expansion."
==Definition==
Let ''A'' be an algebraic structure (in the sense of universal algebra) or equivalently a structure in the sense of model theory, organized as a set ''X'' together with an indexed family of operations and relations φi on that set, with index set ''I''. Then the reduct of ''A'' defined by a subset ''J'' of ''I'' is the structure consisting of the set ''X'' and ''J''-indexed family of operations and relations whose ''j''-th operation or relation for ''j''∈''J'' is the ''j''-th operation or relation of ''A''. That is, this reduct is the structure ''A'' with the omission of those operations and relations φ''i'' for which ''i'' is not in ''J''.
A structure ''A'' is an expansion of ''B'' just when ''B'' is a reduct of ''A''. That is, reduct and expansion are mutual converses.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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