Timeline for The role of the rigid relation principle ($RR$) in the Kunen inconsistency
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 9, 2015 at 13:00 | vote | accept | Thomas Benjamin | ||
| Apr 12, 2015 at 16:45 | |||||
| Apr 8, 2015 at 9:45 | comment | added | Mathieu Baillif | Thanks for your answer. I'd love to give it a shot, but the time I have at disposal (and my scarce knowledge) makes it quite unlikely, unfortunately. | |
| Apr 8, 2015 at 9:11 | history | edited | Thomas Benjamin | CC BY-SA 3.0 |
corrected spelling
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| Apr 8, 2015 at 2:18 | comment | added | Joel David Hamkins | @MathieuBaillif, Unfortunately, this question is still open. Why not give it a shot? There may still be some easy pickings about it... | |
| Apr 7, 2015 at 20:53 | comment | added | Mathieu Baillif | My knowledge of the subject is quite narrow, but out of curiosity, I'd like to ask @JDH about the relationship between RR and the prime ideal axiom. It seems that at the time of publication of the mentioned paper, it was unknown whether one implies the other (or both). Is it still the case ? | |
| Apr 7, 2015 at 19:27 | answer | added | Yair Hayut | timeline score: 7 | |
| Apr 6, 2015 at 17:02 | comment | added | Thomas Benjamin | @JDH: Actually, I had both in mind, but asked the related question because,if I understand correctly, Kunen used the Erdos-Hajnal theorem to prove that in KM, the only elementary embedding j:$V$$\rightarrow$$V$ is the identity (Thm 1 of Kunen (1971)), which suggested to me that $RR$ is certainly needed in the proof. I asked question 3 because I thought that if the Kunen inconsistency could be proved from $NGB+{\lnot}AC+{\lnot}RR$, it would be a very nontrivial result. | |
| Apr 6, 2015 at 14:13 | answer | added | Joel David Hamkins | timeline score: 4 | |
| Apr 6, 2015 at 13:58 | comment | added | Joel David Hamkins | For question 3, I would have expected that you inquire whether the Kunen inconsistency can be proved in $\text{NBG}+\text{RR}$, that is, by weakening the use of $\text{AC}$ in the usual proofs to use merely $\text{RR}$ instead. This version of the question would amount to: can you prove the Kunen inconsistency using only the rigid relation principle instead of the axiom of choice? Is that what you had had in mind, or did you really intend to ask question 3 as you have stated it? | |
| Apr 6, 2015 at 12:14 | history | asked | Thomas Benjamin | CC BY-SA 3.0 |