Timeline for When does every $\infty$-localization correspond to a Bousfield localization?
Current License: CC BY-SA 3.0
6 events
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| Sep 1, 2019 at 12:22 | comment | added | Mike Shulman | Ok - I mentioned it because your answer above suggested that cohomological localization is probably equivalent to Vopenka's principle instead. I haven't looked at this enough to have any thoughts myself. | |
| Sep 1, 2019 at 11:23 | comment | added | David White | @MikeShulman: yes, that's one of my favorite papers. It makes a strong case that the existence of cohomological localizations should be equivalent to the existence of arbitrarily large supercompact cardinals. I'd love to get your thoughts on that at some point. | |
| Aug 31, 2019 at 13:06 | comment | added | Mike Shulman | According to arxiv.org/abs/1101.2792, the existence of cohomological localizations follows from the existence of arbitrarily large supercompact cardinals, which is significantly weaker than Vopenka's principle. | |
| Apr 22, 2018 at 17:37 | vote | accept | Tim Campion | ||
| Jul 20, 2016 at 7:02 | comment | added | Tim Campion | Thanks! Regarding Vopenka's principle (VP), it's known that VP can't be proven in ZFC unless ZFC itself is inconsistent (essentially by Godel's theorem) -- it's the negation of VP that you'd prove if you found a localization that provably didn't exist, which as you say would still be a big result in set theory. When you say "this assumption is ridiculously strong" you mean the assumption that all Bousfield localizations exist, not just small ones, right? Because 5.5 deals with presentable things, which do have combinatorial models, where all small Bousfield localizations exist. | |
| Jul 20, 2016 at 3:12 | history | answered | David White | CC BY-SA 3.0 |