Timeline for For a partition of $\mathbb{R}$ into countably infinite sets, must there be an almost-disjoint family of $2^{\frak c}$ many selectors?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Mar 21, 2015 at 11:42 | comment | added | Joel David Hamkins | @Ashutosh Would it be possible for you to expand on your comment and post an answer? | |
| Mar 21, 2015 at 1:56 | comment | added | Ashutosh | CH wouldn't be sufficient to get $\omega_2$ many almost disjoint selectors. For example, if there is an $\omega_2$-saturated sigma ideal over $\omega_1$. | |
| Mar 20, 2015 at 17:51 | comment | added | Joel David Hamkins | In my previous comment, I meant: almost-disjoint | |
| Mar 20, 2015 at 17:37 | comment | added | Joel David Hamkins | Good, this is progress, showing that we cannot omit CH. But when CH holds, so far you've got only a disjoint family of size $\omega_1$. By my construction, one can push this to $\omega_2$, if there is a Kurepa tree, and to $2^{\omega_1}$, if there is a thick Kurepa tree. But do we really need these Kurepa trees? | |
| Mar 20, 2015 at 17:22 | history | answered | Eric Wofsey | CC BY-SA 3.0 |