Timeline for moving up a consequence of PFA
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 26, 2016 at 3:03 | answer | added | Mohammad Golshani | timeline score: 6 | |
| Apr 26, 2016 at 1:50 | comment | added | user3462 | The paper Two applications of finite side conditions on $\omega_2$ by Neeman also seems to be relevant. See the discussion starting at the bottom of the second page. He considers the problem of adding some sort of specialising function for a single $\omega_2$-tree, and already here there are complications, persistent counterexamples etc. | |
| Apr 25, 2016 at 23:28 | comment | added | user3462 | For example if we could show that it is consistent that every $\omega_2$-tree of size $\aleph_2$ is $\omega_1$-essentially special and $2^{\aleph_1}=\aleph_3$, it seems like this might give the consistency of the statement you are interested in. | |
| Apr 25, 2016 at 23:26 | comment | added | user3462 | I think this result is due to Todorcevic, Some Combinatorial Properties of Trees (answering a question of Abraham from his PhD thesis about whether the negation of the first statement in the question is true in ZFC), where he shows that this follows from the conjunction of $2^{\aleph_0}= \aleph_2$ and every $\omega_1$-tree of size $\aleph_1$ is essentially special. This is Theorem 2. The proof seems like it might be helpful here too. | |
| Apr 25, 2016 at 21:19 | history | asked | Monroe Eskew | CC BY-SA 3.0 |