Timeline for The Set-Theoretic Multiverse and Joint Embeddings
Current License: CC BY-SA 3.0
22 events
| when toggle format | what | by | license | comment | |
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| Mar 30, 2016 at 13:26 | history | edited | Mikhail Katz |
edited tags
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| Dec 30, 2014 at 0:29 | comment | added | Kyle Gannon | @NoahS: That would be nice. I would just like a construction that I can get my hands on (where the property fails, or some similar embedding property fails). | |
| Dec 30, 2014 at 0:00 | comment | added | Noah Schweber | @KyleGannon I am still very curious what you mean by "coherent." Do you mean, "Has a natural model?" | |
| Dec 29, 2014 at 23:34 | answer | added | François G. Dorais | timeline score: 4 | |
| Dec 29, 2014 at 22:58 | answer | added | Joel David Hamkins | timeline score: 4 | |
| Dec 29, 2014 at 22:57 | vote | accept | Kyle Gannon | ||
| Dec 29, 2014 at 23:19 | |||||
| Dec 29, 2014 at 22:50 | comment | added | Kyle Gannon | @NoahS: I know that they are not (usually) equivalent. I was struggling to formalize my question. But I am happy that they actually are equivalent. | |
| Dec 29, 2014 at 22:48 | comment | added | Noah Schweber | @KyleGannon note that the notion you describe is not what is usually meant by interpretability (although the forcing extension axiom makes it equivalent, for the purposes of this question, to interpretability with parameters). | |
| Dec 29, 2014 at 22:47 | comment | added | Noah Schweber | @TimCampion By "the" multiverse I didn't mean the "actual" multiverse; rather, that there's an analogy between "multiverses" and "proper classes of structures." | |
| Dec 29, 2014 at 22:42 | comment | added | Kyle Gannon | @EmilJeřábek: You're absolutely right, I should have called it that. | |
| Dec 29, 2014 at 22:41 | history | edited | Kyle Gannon | CC BY-SA 3.0 |
Changed name
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| Dec 29, 2014 at 22:34 | history | edited | Kyle Gannon | CC BY-SA 3.0 |
Changed name
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| Dec 29, 2014 at 22:34 | comment | added | Emil Jeřábek | The axiom really looks like a variant of the joint embedding property, not of Vopěnka’s principle. | |
| Dec 29, 2014 at 22:32 | comment | added | Tim Campion | If the multiverse is the proper class of models, then the statement should be "there exist $M, N$ such that $M ≺ N$, which is trivial, no? | |
| Dec 29, 2014 at 22:31 | comment | added | Noah Schweber | @KyleGannon, by "coherent" do you mean "consistent?" I thought that at first, but now I'm not quite sure. (Also, I misunderstood you; I've deleted a now-irrelevant comment.) | |
| Dec 29, 2014 at 22:30 | comment | added | Noah Schweber | @TimCampion I think the multiverse is meant to be the analogue of "proper class of models," and interpretations are the morphisms. | |
| Dec 29, 2014 at 22:28 | comment | added | Tim Campion | Curious bystander: How would this be an analogue of Vopenka? I know there are many statements of Vopenka's principle, but the one I'm most familiar with says that if you have a proper class of models, then there's a morphism from one of them to another. I don't see an analogue of the proper class of models here... | |
| Dec 29, 2014 at 22:26 | answer | added | Noah Schweber | timeline score: 3 | |
| Dec 29, 2014 at 22:25 | comment | added | Asaf Karagila♦ | There are several of multiverse notions; Hamkins, Steel, Woodin and Väänänen. Each of them has his own definition of a multiverse (granted, Steel and Woodin were mainly interested in the generic multiverse, but still). It's a real multiverse of multiverses. | |
| Dec 29, 2014 at 22:21 | history | undeleted | Kyle Gannon | ||
| Dec 29, 2014 at 22:19 | history | deleted | Kyle Gannon | via Vote | |
| Dec 29, 2014 at 22:12 | history | asked | Kyle Gannon | CC BY-SA 3.0 |