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”Species”関連
（参考）
URLﾘﾝｸ(www.kurims.kyoto-u.ac.jp)
INTER-UNIVERSAL TEICHMULLER THEORY IV: ¨
LOG-VOLUME COMPUTATIONS AND
SET-THEORETIC FOUNDATIONS
Shinichi Mochizuki
April 2020
P74
Remark 3.3.1.
(i) One well-known consequence of the axiom of foundation of axiomatic set theory is the assertion that “∈-loops”
a ∈ b ∈ c ∈ ... ∈ a
can never occur in the set theory in which one works. On the other hand, there are many situations in mathematics in which one wishes to somehow “identify”
mathematical objects that arise at higher levels of the ∈-structure of the set theory
under consideration with mathematical objects that arise at lower levels of this ∈-structure.
つづく