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 φi for which i is not in J.
Structure A is an expansion of B just when B is a reduct of A. That is, reduct and expansion are mutual converses.
Read more about this topic: Reduct
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