Timeline for Kunen inconsistency with atoms
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 31, 2017 at 17:28 | vote | accept | Beau Madison Mount | ||
| Dec 31, 2017 at 13:55 | comment | added | Joel David Hamkins | But actually, one can also argue without AC in ZF with atoms that every non-identity $j:V\to V$ that fixes all atoms must move ordinals. If $j$ fixes all ordinals, then it fixes $V_\alpha(A)$ for any set of atoms $A$. Now argue by induction on rank that $j$ fixes every element. | |
| Dec 31, 2017 at 12:38 | comment | added | Joel David Hamkins | @Asaf, it seems fine to me to have it be about identity. It follows that there must be ordinals moved. For example, if you well-order a set and all ordinals are fixed, then $j(x)$ would have to be the same as $j"x$, and so there could be no $\in$-minimal set that is moved. | |
| Dec 31, 2017 at 12:37 | answer | added | Joel David Hamkins | timeline score: 11 | |
| Dec 31, 2017 at 10:09 | comment | added | Asaf Karagila♦ | The non-trivial clause should be about ordinals moved. Not about identity. | |
| Dec 31, 2017 at 10:06 | history | edited | Beau Madison Mount | CC BY-SA 3.0 |
added 25 characters in body
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| Dec 31, 2017 at 10:01 | history | asked | Beau Madison Mount | CC BY-SA 3.0 |