Timeline for What can we learn about an elementary embedding from the image of the ordinals?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Feb 26, 2012 at 5:21 | comment | added | Joel David Hamkins | I agree with all that. | |
| Feb 26, 2012 at 5:00 | comment | added | jonasreitz | If we can always recover $j$ from $j''ORD$, then it seems $M[j''ORD]$ could properly contain both $M$ and $V$, and more. | |
| Feb 26, 2012 at 4:58 | comment | added | jonasreitz | Thanks, Joel -- very nice argument! If we drop your condition that $M \subset V$, I think your argument shows we can still recover $V$ but we get $V \subset M[j''ORD]$ instead of equality. Is $V$ a definable class in this case? For this I guess we'd need a more canonical representation of each element -- something like the set $W$ that I described in the question, I'll think about how to make this work. Your argument also shows that we can recover the map $j$ from the image of the ordinals, provided $j$ is definable in $V$. What if $j$ is not 'in $V$', for example an external ultrapower? | |
| Feb 26, 2012 at 4:34 | vote | accept | jonasreitz | ||
| Feb 26, 2012 at 3:28 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
added 679 characters in body
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| Feb 26, 2012 at 2:59 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |