Inter-universal geometry と ABC予想 (応援スレ) 77at MATHInter-universal geometry と ABC予想 (応援スレ) 77 - 暇つぶし2ch■コピペモード□スレを通常表示□オプションモード□このｽﾚｯﾄﾞのURL■項目テキスト250:現代数学の系譜 雑談 25/11/05 10:13:53.81 K/Lr81ky.net つづき （追加）>>247より https://mathoverflow.net/questions/360290/how-strong-a-set-theory-is-necessary-for-practical-purposes-in-sheaf-theory How strong a set theory is necessary for practical purposes in sheaf theory? asked May 14, 2020 user158035 Is it known how much of ZFC is actually necessary for the basic, familiar constructions and theorems in sheaf theory, along the lines of section II.1 (and its exercises) in Hartshorne's "Algebraic Geometry" textbook? 1 Answer Colin McLarty has looked into this The large structures of Grothendieck founded on finite order arithmetic, Review of Symbolic Logic 13 issue 2 (2020) pp. 296--325, doi:10.1017/S1755020319000340, https://arxiv.org/abs/1102.1773 with abstract (emphasis added): The large-structure tools of cohomology including toposes and derived categories stay close to arithmetic in practice, yet published foundations for them go beyond ZFC in logical strength. We reduce the gap by founding all the theorems of Grothendieck’s SGA, plus derived categories, at the level of Finite-Order Arithmetic, far below ZFC. This is the weakest possible foundation for the large-structure tools because one elementary topos of sets with infinity is already this strong. answered May 14, 2020 David Roberts♦ (引用終り) 以上 次ページ最新レス表示レスジャンプ類似スレ一覧スレッドの検索話題のニュースおまかせリストオプションしおりを挟むスレッドに書込スレッドの一覧暇つぶし2ch