Timeline for almost disjoint ladder system on $\omega_2$
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 24, 2015 at 18:58 | vote | accept | Monroe Eskew | ||
| Sep 24, 2015 at 15:45 | answer | added | Péter Komjáth | timeline score: 6 | |
| Sep 23, 2015 at 17:09 | comment | added | Joel David Hamkins | @PéterKomjáth Why not post that as an answer? | |
| Sep 23, 2015 at 17:06 | comment | added | Péter Komjáth | Here is the forcing: assume that `$\{A_\alpha:\alpha<\omega_2\}$ is a collectin of $\aleph_1$-sized sets with countable intersection. The forcing shrinks each of them to an uncountable subset, so that these sets have finite intersections: $p\in P$ if $p$ is a function, $Dom(p)$ is a finite subset of $\omega_2$ and $p(\alpha)$ is a finite subset of $A_\alpha$. $p'$ extends $p$ iff $Dom(p')\supseteq Dom(p)$, $p'(\alpha)\supseteq p(\alpha)$ for $\alpha\in Dom(p)$ and $p'(\alpha)\cap p'(\beta)=p(\alpha)\cap p(\beta)$ for $\alpha,\beta\in Dom(p)$. ccc is the tricky thing. | |
| Sep 23, 2015 at 16:48 | comment | added | Péter Komjáth | Isn't this done in Baumgartner's Almost-disjoint sets, the dense set problem and the partition calculus? Annals of Math. Logic, 10(1976), p. 424, part 6. with the so-called thinning out forcing. | |
| Sep 23, 2015 at 15:55 | history | asked | Monroe Eskew | CC BY-SA 3.0 |