Timeline for Cohen generics over the ground model still Cohen over other generic extensions?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 20, 2018 at 17:39 | vote | accept | Iian Smythe | ||
| Jul 20, 2018 at 13:01 | answer | added | Miha Habič | timeline score: 8 | |
| Jul 19, 2018 at 20:18 | comment | added | Miha Habič | I tried working things like this out around when I asked the linked question, but I didn't get very far. I remember that for the case of Miller forcing, I could show that, given a Cohen $c$, any Miller condition $T\in M$ had a strengthening to a kind of master condition that would force that $c$ remains Cohen over the Miller extension, but it was quite far from working for all $c$ at once. | |
| Jul 19, 2018 at 18:31 | comment | added | Iian Smythe | I am particularly curious about Mathias, Laver and Miller forcing, for what it's worth. | |
| Jul 19, 2018 at 17:25 | comment | added | Joel David Hamkins | It is of course sufficient if every dense subset of $2^{<\omega}$ of $M[G]$ contains a dense subset of $M$, as Todd proves is the case for Sacks forcing. But is this condition also necessary? | |
| Jul 19, 2018 at 17:09 | comment | added | Monroe Eskew | I would guess that you can do this with other perfect-tree-based forcings. | |
| Jul 19, 2018 at 17:03 | comment | added | Monroe Eskew | @JoelDavidHamkins, yep! I didn't know about that. | |
| Jul 19, 2018 at 16:56 | comment | added | Joel David Hamkins | @MonroeEskew Doesn't the Sacks forcing example already refute your "probably fails" remark? | |
| Jul 19, 2018 at 16:26 | comment | added | Monroe Eskew | If $\mathbb P$ does not add reals, this is guaranteed. Otherwise it probably fails. | |
| Jul 19, 2018 at 16:18 | history | asked | Iian Smythe | CC BY-SA 4.0 |