Timeline for How did ZFC become the standard foundations of mathematics?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Oct 6, 2020 at 5:30 | comment | added | Conifold | @NoahSchweber I defer to your expertise on this. Could you suggest an edit (if there is a valid point in the vicinity)? | |
| Oct 6, 2020 at 3:19 | comment | added | Noah Schweber | Moreover, while some models of NFU arise from nonstandard ZF(C) models, I don't think all of them do - so that's also misleading. I think the author is trying to make a point about how the two "flavors" of set theory can each encompass the other but is playing fast-and-loose with the actual details. | |
| Oct 6, 2020 at 3:14 | comment | added | Noah Schweber | @Conifold That's bizarre. Unless I'm having a terribly stupid moment it's definitely not true since ZFC proves the consistency of NFU (to put it mildly). I think that passage is flat-out wrong. | |
| Oct 5, 2020 at 8:22 | comment | added | Conifold | @NoahSchweber SEP's long version:"The NFU world can be understood to be a nonstandard initial segment of the world of ZFC (which could be arranged to include its entire standard part!) with an automorphism and the ZFC world (or an initial segment of it) can be interpreted in NFU as the theory of isomorphism classes of well-founded extensional relations with top (often restricted to its strongly cantorian part); these two theories are mutually interpretable, so the corresponding views of the world admit mutual translation." | |
| Oct 5, 2020 at 2:56 | comment | added | Noah Schweber | NFU is definitely not bi-interpretable with ZFC - it has far too weak consistency strength. (And meanwhile NF is not known to be consistent even relative to large cardinals - there's a claimed relative consistency proof by Holmes, according to which NF would have much weaker consistency strength than ZFC, but as far as I'm aware it hasn't been accepted yet despite being around for a few years now.) | |
| Oct 5, 2020 at 2:54 | comment | added | Noah Schweber | "von Neumann and Fraenkel added axioms of regularity and foundation to 𝑍" Regularity is the same as foundation. Do you mean replacement? | |
| Sep 26, 2020 at 19:04 | history | edited | Conifold | CC BY-SA 4.0 | added 12 characters in body |
| Sep 26, 2020 at 16:22 | comment | added | Alex | This answer is so good I saved it to my PC. | |
| Sep 23, 2020 at 19:10 | history | edited | Conifold | CC BY-SA 4.0 | added 3 characters in body |
| Sep 23, 2020 at 17:40 | vote | accept | Alex | ||
| Sep 23, 2020 at 8:10 | history | edited | Conifold | CC BY-SA 4.0 | added 83 characters in body |
| Sep 23, 2020 at 7:51 | history | edited | Conifold | CC BY-SA 4.0 | added 139 characters in body |
| Sep 23, 2020 at 7:46 | history | answered | Conifold | CC BY-SA 4.0 |