Timeline for Authorship of Grothendieck universes
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Dec 13, 2022 at 17:41 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https (the question was bumped anyway)
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| Nov 2, 2022 at 11:28 | comment | added | Joel David Hamkins | All the more reason to abandon the "Grothendieck universe" terminology... | |
| Nov 2, 2022 at 7:34 | comment | added | Colin McLarty | @JoelDavidHamkins Certainly Grothendieck did not intend any advance in set theory, but a use of set theory advancing algebraic geometry. Having "Bourbaki" sign the appendix on universes in SGA was a signal that there is nothing original in that appendix. The character "Bourbaki" was explicitly an encyclopedist, collecting the best and never introducing anything new. Even at the Bourbaki seminar speakers normally report on other people's results, not their own. | |
| Nov 2, 2022 at 0:06 | comment | added | Colin McLarty | It is fine to call them Zermelo-Grothendieck, or Grothendieck-Zermelo, universes. But Zermelo was also not the first to consider inaccessible cardinals and universes. Hausdorff did that in the Mathematische Annalen in 1908. Tarski and Kuratowski and Baer and Zermelo all followed up on that in the years up to 1930. Steve Givant calls set theory with these universes "Tarski–Grothendieck set theory." Mathematical terminology almost never conveys the full history of concepts. | |
| Nov 1, 2022 at 17:29 | comment | added | Joel David Hamkins | It seems to me that Zermelo's analysis was a far more significant advance in providing the quasi-categoricity result. | |
| Oct 28, 2022 at 15:46 | comment | added | Joel David Hamkins | In particular, in my view category theorists should stop saying Grothendieck universe in favor of the Zermelo-Grothendieck universe terminology. Obviously the idea should have Zermelo's name if it has anyone's name. | |
| Oct 28, 2022 at 15:35 | comment | added | Joel David Hamkins | Yes, evidently Grothendieck was the first to make use of universes in category theory. Meanwhile, the universe concept itself strikes me as fundamentally set-theoretic in nature, even in its use in category theory, which is fundamentally similar to the use in set theory, namely, to delimit a robust realm of mathematical objects and structures, forming a mathematical world of sorts. The universe concept and the universe axiom is the beginning of the large cardinal hierarchy, understood and analyzed most deeply mainly in set theory. | |
| Oct 28, 2022 at 15:21 | comment | added | user234212323 | I think that if we are talking about Grothendieck, we mean implicitly categorical language. In that sense, it is fair to say that Grothendieck introduced the notion in categorical foundations. I was of the supposition that it was Tarski who introduced the notion before, but you clarified its introduction in set-theoretical foundations. The question goes in the direction of Grothendieck' seminar and in that way into categorical foundations. Thanks for your clarification, nevertheless. | |
| Oct 28, 2022 at 2:08 | history | answered | Joel David Hamkins | CC BY-SA 4.0 |