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An inductive definition of a set S is as follows, where B is a set of 0-ary rules and I is a set of rules of positive arity:
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Basis: if b is a rule in B then b() is an element of S.
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Induction: if (x1,...,xn) is a tuple of elements of S and i is an n-ary rule in I that can be applied to (x1,...,xn) then i(x1,...,xn) is an element of S.
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Closure: any element in S results from applying finitely many times rules in B or in I.
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As the closure part of the definition is always the same, its is usually omitted, as in the sequel.
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