Timeline for Vopěnka's Principle for non-first-order logics
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Aug 21, 2022 at 2:31 | vote | accept | Noah Schweber | ||
| Apr 15, 2021 at 8:27 | history | edited | Asaf Karagila♦ | CC BY-SA 4.0 |
Seeing how a new answer was posted, might as fix this minor issue.
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| Apr 14, 2021 at 13:47 | answer | added | Will Boney | timeline score: 3 | |
| Mar 8, 2021 at 22:47 | comment | added | Noah Schweber | @TimCampion Generality isn't inherently good. I personally think "regular logic" captures a very natural level of generality. | |
| Mar 8, 2021 at 22:46 | comment | added | Tim Campion | Okay. If Ebbinghaus and Flum's definition doesn't include propositional logics, I might want to find a more flexible definition, but I suppose that's a matter of taste. | |
| Mar 8, 2021 at 22:43 | comment | added | Noah Schweber | @TimCampion Propositional logics aren't regular logics in the sense of the question, though. | |
| Mar 8, 2021 at 22:42 | comment | added | Tim Campion | For a trivial lower bound, note that if $\mathcal L$ is pretty much any form of (set-sized) propositional logic, then $VP(\mathcal L)$ is a theorem of ZFC: there are only set-many models, so if you have a class of them two must agree. | |
| Mar 8, 2021 at 22:04 | history | edited | Noah Schweber |
edited tags
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| Sep 6, 2018 at 23:54 | comment | added | Tim Campion | The statement attributed to Friedman in 2005 in the question and many similar statements too were already systematically studied in Ch 6 of Adamek and Rosicky's 1994 book Locally Presentable and Accessible Categories. For a lower bound, they show for example that Vopenka's principle is equivalent to the statement that for any proper class of graphs, one embeds (not elementarily) in another. At the upper end, Vopenka's principle implies that for any proper class of objects in an accessible category, one admits a nonidentity map to another. This includes all AECs for example. | |
| Jul 18, 2015 at 15:57 | answer | added | Thomas Benjamin | timeline score: 11 | |
| Aug 8, 2013 at 4:04 | answer | added | Joel David Hamkins | timeline score: 9 | |
| Aug 8, 2013 at 1:36 | comment | added | Andrés E. Caicedo | Issues closely related to more precise consistency strength bounds are addressed by Norman Perlmutter, see his recent preprint The large cardinals between supercompact and almost-huge. In particular, he shows that a cardinal is Vopěnka iff it is Woodin-for-supercompactness (as suggested by Kanamori). | |
| Aug 8, 2013 at 1:19 | history | edited | Noah Schweber | CC BY-SA 3.0 |
added 9 characters in body
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| Aug 7, 2013 at 23:36 | history | asked | Noah Schweber | CC BY-SA 3.0 |