>>913
>正則性の格子点に反するのだから無限シングルトンなるもの使うならもはやZFは使えない

https://ja.wikipedia.org/wiki/%E6%AD%A3%E5%89%87%E6%80%A7%E5%85%AC%E7%90%86
正則性公理（せいそくせいこうり、英: axiom of regularity）は、別名基礎の公理（きそのこうり、英: axiom of foundation） とも呼ばれ、ZF公理系を構成する公理の一つで、1925年にジョン・フォン・ノイマンによって導入された。
https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory
Zermelo?Fraenkel set theory
History
In 1908, Ernst Zermelo proposed the first axiomatic set theory, Zermelo set theory.
However, as first pointed out by Abraham Fraenkel in a 1921 letter to Zermelo, this theory was incapable of proving the existence of certain sets and cardinal numbers whose existence was taken for granted by most set theorists of the time, notably the cardinal number ｱﾚﾌ _ω and the set {Z_{0},P(Z_{0}),P(P(Z_{0})),P(P(P(Z_{0}))),...}, where Z_{0} is any infinite set and P is the power set operation.[2]
Moreover, one of Zermelo's axioms invoked a concept, that of a "definite" property, whose operational meaning was not clear.
In 1922, Fraenkel and Thoralf Skolem independently proposed operationalizing a "definite" property as one that could be formulated as a well-formed formula in a first-order logic whose atomic formulas were limited to set membership and identity.
They also independently proposed replacing the axiom schema of specification with the axiom schema of replacement.
(引用終り)

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