906 名前:１３２人目の素数さん [sage] :2021/12/28(火) 20:55:56.10 ID:IQKnQwAx
>>886
>なお、∈の「ループ」については、望月氏の和文のIUT入門講義資料の中で言及していて
>”∈の「ループ」そのものではないが、∈の「ループ」類似を考える”みたいな記述があったよ
>（後で探してみる）
>だから、「”∈の「ループ」そのもの”は、基礎の公理に反す」までは、望月氏は自覚あるよ

「”∈の「ループ」そのもの”は、基礎の公理に反す」は、下記のIUT IVでした（和文ではなかった）
関連箇所を引用しておくよ

https://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20IV.pdf
INTER-UNIVERSAL TEICHMULLER THEORY IV:
LOG-VOLUME COMPUTATIONS AND
SET-THEORETIC FOUNDATIONS
Shinichi Mochizuki
April 2020

P5
If, moreover, one thinks of Z as being constructed, in the usual way, via axiomatic set theory, then one may interpret the “absolute” - i.e., “tautologically
unrelativizable” - nature of conventional scheme theory over Z at a purely settheoretic level. Indeed, from the point of view of the “∈-structure” of axiomatic set
theory, there is no way to treat sets constructed at distinct levels of this ∈-structure
as being on a par with one another. On the other hand, if one focuses not on
the level of the ∈-structure to which a set belongs, but rather on species, then the
notion of a species allows one to relate - i.e., to treat on a par with one another -
objects belonging to the species that arise from sets constructed at distinct levels
of the ∈-structure. That is to say,
the notion of a species allows one to “simulate ∈-loops” without violating the axiom of foundation of axiomatic set theory
- cf. the discussion of Remark 3.3.1, (i).

P68
On the other hand, by the axiom of
foundation, there do not exist infinite descending chains of universes
V0 V1 V2 V3 ... Vn ...
- where n ranges over the natural numbers.

つづく