Formal Definition
A recursive definition of a hereditarily finite set goes as follows:
- Base case: The empty set is a hereditarily finite set.
- Recursion rule: If a1,...,ak are hereditarily finite, then so is {a1,...,ak}.
The set of all hereditarily finite sets is denoted Vω. If we denote P(S) for the power set of S, Vω can also be constructed by first taking the empty set written V0, then V1 = P(V0), V2 = P(V1),..., Vk = P(Vk−1),... Then
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