>>86 Zermelo set theory (sometimes denoted by Z-) https://en.wikipedia.org/wiki/Zermelo_set_theory ここで、Zermelo set theoryで批判されているのは、ノイマン構成に比べてのこと Zermeloでは、空集合Φ={}から始まって、Φ={},{{}},{{{}}},・・と全ての自然数が出来て ω(=N)＝{0,1,2,・・}ができるとする（Φ={}→0,{{}}→1,{{{}}}→2,など）
ここから、{ω},{{ω}},{{{ω}}},・・とできるけど、 ”In the usual cumulative hierarchy Vα of ZFC set theory (for ordinals α), any one of the sets Vα for α a limit ordinal larger than the first infinite ordinal ω (such as Vω・2) forms a model of Zermelo set theory. So the consistency of Zermelo set theory is a theorem of ZFC set theory. Zermelo's axioms do not imply the existence of ｱﾚﾌω or larger infinite cardinals, as the model Vω・2 does not contain such cardinals. (Cardinals have to be defined differently in Zermelo set theory, as the usual definition of cardinals and ordinals does not work very well: with the usual definition it is not even possible to prove the existence of the ordinal ω2.)” などと批判されているよね
