Timeline for Definition of "galaxy", due to Sabbagh/Samuel
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 30, 2023 at 23:23 | comment | added | David Roberts♦ | @uhoh thanks! ^_^ | |
| Nov 30, 2023 at 22:04 | comment | added | uhoh | just fyi I've mentioned your Terry Tao’s first paper: “Perfect numbers” in HSM SE | |
| Aug 30, 2022 at 1:24 | comment | added | David Roberts♦ | @Monroe it turns out the interest dates back to how Bourbaki was going to deal with categories, I believe Lacombe was consulted and co-wrote something with Samuel; definitely at some point he wrote up a document giving various options. There's records of Bourbaki discussions where Grothendieck didn't like the idea of class-set theory, and pushed for universes instead. | |
| Aug 30, 2022 at 1:18 | vote | accept | David Roberts♦ | ||
| Aug 29, 2022 at 16:21 | answer | added | David Roberts♦ | timeline score: 3 | |
| Aug 26, 2022 at 16:18 | answer | added | Sabbagh | timeline score: 9 | |
| Jun 24, 2022 at 12:42 | comment | added | David Roberts♦ | @MonroeEskew perhaps you should ask a fresh MO question about all this, rather than me, on my question, which is deliberately rather narrow in scope :-) | |
| Jun 24, 2022 at 7:36 | comment | added | Monroe Eskew | I would be less perplexed if the same people also were cataloguing exactly how complex of formulae they were using with Replacement and Comprehension, or whether the full Powerset axiom was needed, etc. To illustrate my point, it is rare to find a mathematician who is deeply interested in Harvey Friedman's RM result about Borel determinacy, but much more common to find one who wants to know a proof of Borel determinacy, or apply it. | |
| Jun 24, 2022 at 7:27 | comment | added | Monroe Eskew | The reason for my question is to understand the motivations and philosophy. Although RM is "a thing", my impression is that most mathematicians are not Reverse but Forward, meaning they primarily care about proving new results and reaching a new understanding of a topic and knowing what's true, rather than investigating what axioms or fragments of schema are needed for a result. So when people start using universes to prove things but then get worried about going beyond ZFC, this seems like this is a relatively isolated concern rather than part of a pattern of being an RMer. | |
| Jun 24, 2022 at 2:07 | comment | added | David Roberts♦ | @MonroeEskew I don't understand the reason for your questions. Reverse Mathematics is a thing. Mathematicians have been wondering about what axioms are really needed for theorems since ancient Greece.... I'm asking for a source and/or a definition of something that is a prehistoric ancestor of the way Clausen and Scholze's condensed mathematics deals with size issues. | |
| Jun 23, 2022 at 20:19 | comment | added | Monroe Eskew | But why the strong interest in restricting oneself to “standard axioms” if some natural extension makes things easier? Are most mathematicians just that curious about consistency strength hierarchies? | |
| Jun 23, 2022 at 13:27 | comment | added | David Roberts♦ | @MonroeEskew yes, but most mathematicians are not set theorists for whom measurable cardinals and larger are no big deal. It's not about being "afraid", but wanting to know if the de facto standard axioms for maths are actually sufficient to do generic mathematics. | |
| Jun 23, 2022 at 12:20 | comment | added | Monroe Eskew | Why are people so afraid of inaccessibles? Sure they have higher consistency strength, thus "might be" inconsistent from the perspective of ZFC, but in the grand scheme of things from the set theorists' perspective, they are relatively innocuous. | |
| Jun 23, 2022 at 7:22 | comment | added | David Roberts♦ | I don't have Samuel's Collected Papers, and looking on MathSciNet at his papers around 1963, there's nothing that jumps out as possibly containing this "galaxy" stuff (Google searches don't turn up anything useful, either). | |
| Jun 23, 2022 at 7:08 | history | asked | David Roberts♦ | CC BY-SA 4.0 |