Timeline for Does allowing Ur-elements in $\sf ZF^*GC$ break bi-interpretability with $\sf ZF^*GC$?
Current License: CC BY-SA 4.0
7 events
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| Nov 4, 2023 at 0:19 | comment | added | Joel David Hamkins | Ali, I had also tried to answer the question with rigidity issues (before you had posted), but had realized the problematic issue of respecting the choice function. I wonder whether we need to make to more duplication than just urelements, but duplicate every set, in such a way that every possible choice is realized by C in a copy of the given set. This might lessen the role of C somewhat and enable a rigidity argument, but I haven't been able to push it through. I think they might be bi-interpretable. | |
| Nov 3, 2023 at 22:22 | history | edited | Ali Enayat | CC BY-SA 4.0 |
Withdrew the proposed answer.
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| Nov 3, 2023 at 22:00 | comment | added | Ali Enayat | @JoelDavidHamkins Thanks for the prompt correction Joel. I will soon revise. | |
| Nov 3, 2023 at 20:25 | comment | added | Joel David Hamkins | Swapping the urelements a,b, will not induce an automorphism of the structure with the choice function, since the choice function C will choose one of them from {a,b}. | |
| Nov 3, 2023 at 19:01 | vote | accept | Zuhair Al-Johar | ||
| Nov 3, 2023 at 22:30 | |||||
| Nov 3, 2023 at 18:56 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
added 7 characters in body
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| Nov 3, 2023 at 18:39 | history | answered | Ali Enayat | CC BY-SA 4.0 |