Timeline for Destroying Suslin, nothing special
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 10, 2019 at 10:18 | comment | added | Asaf Karagila♦ | Here is a technical refinement to your remark, by the way: Is it consistent that every Aronszajn tree is special, or contains a Suslin subtree? | |
| Dec 19, 2018 at 16:02 | vote | accept | Asaf Karagila♦ | ||
| Dec 2, 2018 at 8:40 | comment | added | Asaf Karagila♦ | Ohh, right. Sorry. | |
| Dec 1, 2018 at 22:55 | comment | added | Jing Zhang | I'm saying you can't have universe where the only A-trees are either special or Suslin (and there is a Suslin tree). You can find other A-trees that are nonspecial and non-Suslin. | |
| Dec 1, 2018 at 22:52 | comment | added | Asaf Karagila♦ | I don't understand. If you added a Suslin tree, how are there no Suslin trees? | |
| Dec 1, 2018 at 22:50 | comment | added | Jing Zhang | You can't achieve this by $\sigma$-closed forcing by Easton's lemma. For the bonus question, you can build a nonspecial non-Suslin tree as follows: start with an special A-tree with some uncountable mac and a Suslin tree, then replace the cone above each element in the mac by the Suslin tree. It is not Suslin since we start with an uncountable mac. It is nonspecial since forcing with this does not collapse $\omega_1$. | |
| Nov 30, 2018 at 16:47 | answer | added | Todd Eisworth | timeline score: 10 | |
| Nov 30, 2018 at 15:17 | history | asked | Asaf Karagila♦ | CC BY-SA 4.0 |