Timeline for Do Grothendieck universes matter for an algebraic geometer?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 12, 2021 at 16:22 | comment | added | Andreas Blass | @YemonChoi is right. If doofoi were the plural, then the singular should be doofos. | |
| May 14, 2019 at 16:49 | comment | added | Noah Schweber | @Wojowu That's true of course. | |
| May 14, 2019 at 9:39 | comment | added | Wojowu | Remark regarding the first of the two bullet points at the end: I am fairly certain it is not even possible to express the full reflection principle in the language of ZFC, because of Tarski's undefinability theorem. $Sigma_n$-reflection is not a statement uniform in $n$. | |
| May 14, 2019 at 2:18 | comment | added | David Roberts♦ | Or doofopodes :-) | |
| May 14, 2019 at 0:15 | comment | added | Yemon Choi | @NoahSchweber I'd have gone with "doofi" myself :) | |
| May 13, 2019 at 22:37 | comment | added | Noah Schweber | @TimothyChow I'm also proud of "doofoi." | |
| May 13, 2019 at 22:36 | comment | added | Timothy Chow | @NoahSchweber : What I am most impressed by is that you used a word ("doofositude") that I understood the meaning of immediately, yet which gets zero Google hits. | |
| May 13, 2019 at 21:47 | comment | added | Noah Schweber | @Gro-Tsen Oh I would certainly bet large sums of money that that's true, but I can't actually claim meaningful confidence there (cf. my previous comment re: local doofositude). | |
| May 13, 2019 at 21:12 | comment | added | Gro-Tsen | In fact, I very much doubt that there's a single instance where Grothendieck universes are used where it wouldn't suffice to have a model of, say, ZFC with Replacement limited to $\Sigma_1$ formulas (let's keep full Separation to be sure); and for this, the $V_δ$ where $δ$ is a fixed point of $α\mapsto\beth_α$ provide a good supply. In what usual mathematical reasoning would such a $V_δ$ not suffice as a “universe”? (OK, maybe let $δ$ be of uncountable cofinality to get closure under sequences as well.) Who ever uses (uncountable) $\Sigma_2$ replacement outside of set theory? | |
| May 13, 2019 at 17:39 | history | edited | Noah Schweber | CC BY-SA 4.0 |
added 945 characters in body
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| May 13, 2019 at 17:26 | history | answered | Noah Schweber | CC BY-SA 4.0 |