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  "body": "\n## Summary\n\nA substructure of a [[structure|983GZBQYT4]] is a subset of its domain that is closed under the functions and contains the constants.\nEach symbol is interpreted on it by restriction.\nIt is the common form of subgroups, subrings and induced subgraphs.\nWhich subsets are substructures depends on the signature, not only on the structure.\n\n## Explanations\n\n### L1 human\n\nTake a structure and keep only some of its elements.\nIf applying the operations to kept elements always gives kept elements, and the constants are kept, the kept part is again a structure of the same kind.\nFor example, the even integers with addition, negation and $0$ form a substructure of $(\\Z, +, -, 0)$.\nIn a graph seen as a structure with one edge relation, any nonempty set of vertices with the edges between them is a substructure.\n",
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