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In set theory, a foundational relation on a set or proper class lets each nonempty subset admit a relational minimal element. Formally, let (A, R) be a binary relation structure, where A is a class (set or proper class), and R is a binary relation defined on A. Then (A, R) is a foundational relation if any nonempty subset in A has an R-minimal element. In predicate logic, in which denotes the empty set.Here is an R-minimal element in the subset S, since none of its R-predecessors is in S.
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