Timeline for Has any open/difficult problem in ordinary mathematics been solved only/mostly by appeal to set theory?
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8 events
| when toggle format | what | by | license | comment | |
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| Oct 26, 2020 at 22:49 | comment | added | Carl-Fredrik Nyberg Brodda | @PeterLeFanuLumsdaine Yes, there is some ambiguity (but I think your interpretation makes for a lot more interesting answers -- such as this one!). | |
| Oct 26, 2020 at 22:32 | comment | added | Peter LeFanu Lumsdaine | @Carl-FredrikNybergBrodda: I guess that sentence from the question — “solved mostly/only because of the insight that set theory has offered” — is ambiguous. I understood it to mean “the solution was mostly/only possible because of set theory”, i.e. “the set theory is essential, or at least hard to avoid”, making this a very apt answer. But I guess your reading “the solution consists mostly/only of set theory” is also reasonable. | |
| Oct 26, 2020 at 22:08 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Oct 26, 2020 at 13:55 | comment | added | Carl-Fredrik Nyberg Brodda | @AndrésE.Caicedo I agree that the set theory is essential as well! That both the group theory and set theory are essential is exactly my point: thus this problem was not (it seems to me) solved mostly/only because of the insight that set theory has offered. | |
| Oct 26, 2020 at 13:49 | comment | added | Andrés E. Caicedo | On the contrary. This shows that the problem is a genuine question from the field it comes from (in this case, group theory), rather than a set-theoretic question in disguise. The set theory is essential as well, that is, only using group-theoretic arguments is not enough. | |
| Oct 26, 2020 at 11:15 | comment | added | Carl-Fredrik Nyberg Brodda | Shelah's involves a great deal of combinatorial group theory (including amalgamated free products and small cancellation theory) quite explicitly. So I'm not sure it satisfies that this problem "has been solved mostly/only because of the insight that set theory has offered". | |
| Oct 26, 2020 at 10:42 | history | edited | Asaf Karagila♦ | CC BY-SA 4.0 |
With apologies to Juris.
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| Oct 26, 2020 at 9:47 | history | answered | Asaf Karagila♦ | CC BY-SA 4.0 |