Timeline for Forcing with c.c.c forcing notions, Cohen reals and Random reals
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| Dec 8, 2016 at 4:50 | history | undeleted | Mohammad Golshani | ||
| Feb 25, 2014 at 4:04 | history | deleted | Mohammad Golshani | via Vote | |
| Nov 20, 2013 at 4:03 | comment | added | Mohammad Golshani | Thanks a lot for you historical information. I think the theorem is just a simple observation, and I arrived to it, not by thinking on the above problem, but on "Foreman's maximality principle" which says "any non-trivial forcing notion either adds a real or collapses some cardinals". Note that a trivial consequence of this principle is that any non-trivial c.c.c. forcing adds a real. | |
| Nov 19, 2013 at 18:39 | comment | added | Andreas Blass | I believe the theorem in your question was proved by Jim Baumgartner. I know that it was proved by me, quite some time ago, but then I was told that Jim had proved it considerably earlier yet. | |
| Nov 6, 2013 at 10:52 | history | undeleted | Mohammad Golshani | ||
| Nov 6, 2013 at 5:20 | history | deleted | Mohammad Golshani | via Vote | |
| Nov 5, 2013 at 6:02 | history | edited | Mohammad Golshani | CC BY-SA 3.0 |
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| Nov 5, 2013 at 5:07 | history | edited | Mohammad Golshani | CC BY-SA 3.0 |
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| Nov 5, 2013 at 3:57 | history | undeleted | Mohammad Golshani | ||
| Nov 5, 2013 at 3:56 | history | deleted | Mohammad Golshani | via Vote | |
| Nov 3, 2013 at 11:26 | comment | added | Haim | Check also the paper "Ccc forcing and splitting reals" by Velickovic, according to which every Suslin ccc forcing adds a Cohen real or is a Maharam algebra. It's also worth mentioning that the question whether every Maharam algebra is a measure algebra was answered negatively by Talagrand. | |
| Nov 3, 2013 at 11:22 | comment | added | Haim | The question whether every Suslin ccc forcing notion adding a real must add a Cohen real or add a random real is problem 4.7 in Shelah's "On what I do not understand": shelah.logic.at/files/666.pdf | |
| Nov 3, 2013 at 7:47 | comment | added | Mohammad Golshani | One can show that Mathias forcing relative to an ultrafilter U adds Cohen reals exactly when U is not selective. | |
| Nov 3, 2013 at 7:20 | comment | added | Monroe Eskew | What about "Prikry reals"? Fix an ultrafilter U on $\omega$, and let $(s,A) \in \mathbb{P}$ when $s$ is finite, $A \in U$, etc., same as Prikry forcing. This is obviously c.c.c., so do you know if it is consistent that Prikry real forcing adds a Cohen real or Random real? | |
| Nov 3, 2013 at 6:54 | history | asked | Mohammad Golshani | CC BY-SA 3.0 |