>>34 追加
https://ja.wikipedia.org/wiki/%E9%81%BA%E4%BC%9D%E7%9A%84%E6%9C%89%E9%99%90%E9%9B%86%E5%90%88
遺伝的有限集合
https://en.wikipedia.org/wiki/Hereditarily_finite_set
Hereditarily finite set
Representation
This class of sets is naturally ranked by the number of bracket pairs necessary to represent the sets:
・{} (i.e.Φ, the Neumann ordinal "0"),
・{{}} (i.e. {Φ} or {0}, the Neumann ordinal "1"),
・{{{}}},
・{{{{}}}} and then also {{},{{}}} (i.e. {0,1}, the Neumann ordinal "2"),
・{{{{{}}}}}, {{{},{{}}}} as well as {{},{{{}}}},
・... sets represented with 6 bracket pairs, e.g. {{{{{{}}}}}},
・... sets represented with 7 bracket pairs, e.g. {{{{{{{}}}}}}},
・... sets represented with 8 bracket pairs, e.g. {{{{{{{{}}}}}}}} or {{},{{}},{{},{{}}}} (i.e. {0,1,2}, the Neumann ordinal "3")
... etc.
In this way, the number of sets with n}n bracket pairs is[1] 1,1,1,2,3,6,12,25,52,113,247,548,1226,2770,6299,14426,・・・
Axiomatizations
ZF
The hereditarily finite sets are a subclass of the Von Neumann universe. Here, the class of all well-founded hereditarily finite sets is denoted Vω. Note that this is also a set in this context.
If we denote by p(S) the power set of S, and by V0 the empty set, then Vω can be obtained by setting V1 = p(V0), V2 = p(V1),..., Vk = p(Vk-1),... and so on.
Thus, Vω can be expressed as Vω=∪ k=0〜∞ Vk.
We see, again, that there are only countably many hereditarily finite sets: Vn is finite for any finite n, its cardinality is n-12 (see tetration), and the union of countably many finite sets is countable.
(引用終り)

遺伝的有限集合、Hereditarily finite set
「naturally ranked by the number of bracket pairs」で
そのbracket（カッコ）の深さのシングルトン達、例えば深さ6 with 6 bracket pairs, e.g. {{{{{{}}}}}}とか出てくるよ
そして、ZFでは、Vω=∪ k=0〜∞ Vk だ
だから、ω重シングルトン あるんじゃね？