Timeline for Direct limits of $\sigma$-centered forcing notions
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| May 21, 2020 at 8:58 | comment | added | Otto | Can't you take a strongly proper forcing $P$ of size $\aleph_1$ that is not c.c.c, then consider some increasing internally approachable countable elementary submodels $\langle M_\alpha: \alpha<\omega_1\rangle$, then $\langle P\cap M_\alpha: \alpha<\omega_1\rangle$ seems to work. | |
| Mar 23, 2019 at 1:28 | comment | added | dragoon | @Goldstern The most natural (but in this case artificial) is, under $\text{MA}_{\aleph_1}$, $C*T$ where $C$ is Cohen forcing and $T$ is the Suslin tree it adds (recall that $\text{MA}_{\aleph_1}$ implies that any poset of size $\aleph_1$ is $\sigma$-centered). Now, assuming $\text{MA}_{\aleph_1}$, perform a finite support iteration of length $\omega_2$ using $C*T$. I wonder whether the resulting poset is $\sigma$-centered | |
| Mar 18, 2019 at 15:15 | comment | added | Goldstern | Can you give an example of a composition $P*Q$ which is $\sigma$-centered, where $P$ forces that $Q$ is not $\sigma$-centered? | |
| Mar 9, 2018 at 0:53 | comment | added | Not Mike | I feel like there is a counter-example arising from something like, the failure of uniformization for a ladder-system on $\omega_1$. However a specific example escapes me at the moment. | |
| Mar 8, 2018 at 10:52 | history | edited | dragoon | CC BY-SA 3.0 |
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| Mar 8, 2018 at 10:19 | history | asked | dragoon | CC BY-SA 3.0 |