Timeline for The Set-Theoretic Multiverse and Joint Embeddings
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Dec 29, 2014 at 23:59 | history | edited | Noah Schweber | CC BY-SA 3.0 |
added 98 characters in body
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| Dec 29, 2014 at 23:56 | comment | added | Joel David Hamkins | Probably, and I expect so, but I don't see it as immediate. After all, it was some work even to get uncountable models that were incomparable by embeddability at all. | |
| Dec 29, 2014 at 23:53 | comment | added | Noah Schweber | I was visualizing a pair of multiverses all of whose elements were uncountable universes (with illfounded $\omega$); I'm pretty sure that we can get a failure of joint embeddability with such a pair. Is this not the case? | |
| Dec 29, 2014 at 23:02 | comment | added | Joel David Hamkins | I don't understand the claim of your first paragraph. If one takes the union of two multiverses of countable models, it will still satisfy the desired joint embedding property, because of my theorem on the fact that countable models are always comparable by embeddability (the multiverses must have models with nonstandard ordinals, and hence there will be universal objects there). Could you explain what you had in mind? | |
| Dec 29, 2014 at 22:57 | vote | accept | Kyle Gannon | ||
| Dec 29, 2014 at 23:19 | |||||
| Dec 29, 2014 at 22:29 | comment | added | Noah Schweber | Although of course in the second paragraph, I'm assuming that by "interpretable" you mean "interpretable with parameters." If you mean parameter-free interpretability, then I'm pretty sure the answer goes back to "no." | |
| Dec 29, 2014 at 22:26 | history | answered | Noah Schweber | CC BY-SA 3.0 |