Timeline for When does Vopěnka's principle hold?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Feb 4, 2021 at 1:30 | comment | added | Tim Campion | An equivalent formulation of VP says that for any Ord-indexed sequence $(A_\alpha)_{\alpha <Ord}$ of objects of $\mathcal C$, there exists $\alpha < \beta$ and a morphism $A_\alpha \to A_\beta$. E.g. in Adamek-Rosicky, this is one of the first equivalent statements shown. (The flexibility about which $\mathcal C$ you assert this for while getting an equivalent to VP is similar to the original formulation.) This formulation is stronger and I think more natural since one needn't think about rigid objects. I don't know how similar the variant of Noah's question using this formulation would be. | |
| Apr 23, 2015 at 5:06 | comment | added | Noah Schweber | @AsafKaragila yes, that's why I say that the pure sets provide a trivial example. | |
| Apr 23, 2015 at 5:06 | history | edited | Noah Schweber | CC BY-SA 3.0 |
added 44 characters in body
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| Apr 23, 2015 at 5:05 | comment | added | Noah Schweber | @JoelDavidHamkins quite right, fixed. | |
| Apr 22, 2015 at 18:37 | answer | added | Joel David Hamkins | timeline score: 15 | |
| Apr 22, 2015 at 18:11 | comment | added | Joel David Hamkins | Noah, I guess in the definition of satisfies VP, you want to insist that $\cal D$ and $\cal C$ are proper classes, rather than merely classes. | |
| Apr 22, 2015 at 14:40 | comment | added | Asaf Karagila♦ | Probably too trivial, but in the language of equality we can prove Vopenka's Principle. | |
| Apr 22, 2015 at 13:15 | answer | added | Joel David Hamkins | timeline score: 11 | |
| Apr 22, 2015 at 13:14 | history | edited | Emil Jeřábek | CC BY-SA 3.0 |
fix spelling
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| Apr 22, 2015 at 12:41 | history | asked | Noah Schweber | CC BY-SA 3.0 |