Timeline for Representation of meager sets in Cohen extensions
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| May 27, 2016 at 21:05 | comment | added | Paul Larson | I think the idea is that, given that $\{ x \in p : B_{x} \text{ is not meager}\}$ is meager, we can find a Borel meager set $C$ containing it, and then subtract $C \times 2^{\omega}$ from $B$. Then we can apply Kuratowski-Ulam to the Borel set $B \setminus (C \times 2^{\omega})$ to see that this set is what we want. | |
| Apr 23, 2016 at 14:05 | comment | added | Carlos | Thank you!, but you are not choosing $B$ in any particular way, and in general, $B$ is not necessarily meager. Consider the trivial case in which $A=\emptyset$. You can take $p\subset B_0=\{x\in {}^\omega2 : x(0)=0\}$ and $B=B_1\times{}^\omega 2$. Then $p \Vdash B_{\mathring{c}} = \mathring{A}$, but $B$ is not meager. | |
| Apr 23, 2016 at 2:58 | review | First posts | |||
| Apr 23, 2016 at 6:08 | |||||
| Apr 23, 2016 at 2:57 | history | answered | Prince | CC BY-SA 3.0 |