現代数学の系譜工学物理雑談古典ガロア理論も読む80

[過去ﾛｸﾞ] 現代数学の系譜工学物理雑談古典ガロア理論も読む80 (1002ﾚｽ)
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171: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE  [] 2020/01/08(水) 11:27:25.70 ID:1QCooAdl

>>170 追加

”the emphasis on the types ("species") of objects”（下記）って、なんですかね？
あんまし、説得力ないと思う
それより、圏論的説明をしっかりやるべきでは？（＾＾；
（"species"って、マイナーな印象しか受けない。数学のメインストリームじゃないでしょ？）

https://en.wikipedia.org/wiki/Inter-universal_Teichm%C3%BCller_theory
Inter-universal Teichmuller theory
(抜粋)
History
In March 2018, Peter Scholze and Jakob Stix visited Kyoto University for five days of discussions with Mochizuki and Yuichiro Hoshi; while this did not resolve the differences, it brought into focus where the difficulties lay.[8][10]

In September 2018, Mochizuki wrote a 41-page summary of his view of the discussions and his conclusions about which aspects of his theory he considers misunderstood.[12] In particular he names:
・"re-initialization" of (mathematical) objects, making their previous "history" inaccessible;
・"labels" for different "versions" of objects;
・the emphasis on the types ("species") of objects.

Google訳
2018年9月、望月は彼の議論の見解と彼の理論のどの側面が誤解されていると考えるかについての結論の41ページの要約を書いた。[12]特に彼は次のように名前を付けています。
・（数学）オブジェクトの「再初期化」。以前の「履歴」にアクセスできなくなります。
・オブジェクトのさまざまな「バージョン」の「ラベル」。
・オブジェクトのタイプ（「種」）の強調。

http://rio2016.5ch.net/test/read.cgi/math/1578091012/171

173: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE  [] 2020/01/08(水) 11:58:02.25 ID:1QCooAdl

>>171 追加

http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20IV.pdf
IUTそのIV
(抜粋)
P68
In the following discussion, we use the phrase “set-theoretic formula” as it is
conventionally used in discussions of axiomatic set theory [cf., e.g., [Drk], Chapter 1,
§2], with the following proviso: In the following discussion, it should be understood
that every set-theoretic formula that appears is “absolute” in the sense that its
validity for a collection of sets contained in some universe V relative to the model
of set theory determined by V is equivalent, for any universe W such that V ∈ W,
to its validity for the same collection of sets relative to the model of set theory
determined by W [cf., e.g., [Drk], Chapter 3, Definition 4.2].
Definition 3.1.
(i) A 0-species S0 is a collection of conditions given by a set-theoretic formula
P85
Bibliography
[Drk] F. R. Drake, Set Theory: an Introduction to Large Cardinals, Studies in Logic
and the Foundations of Mathematics 76, North-Holland (1974).

https://www.researchgate.net/publication/270260913_Drake_Frank_R_Set_theory_An_introduction_to_large_cardinals_Studies_in_logic_and_the_foundations_of_mathematics_vol_76_North-Holland_Publishing_Company_Amsterdam_and_London_and_American_Elsevier_Publi
researchgate
Drake Frank R.. Set theory. An introduction to large cardinals. Studies in logic and the foundations of mathematics, vol. 76. North-Holland Publishing Company, Amsterdam and London, and American Elsevier Publishing Company, Inc., New York, 1974, xii + 351 pp.

http://rio2016.5ch.net/test/read.cgi/math/1578091012/173

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