Timeline for Cohen algebra (generalization)
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 2, 2013 at 1:00 | vote | accept | Rina Shora | ||
| Apr 30, 2013 at 10:52 | comment | added | Rina Shora | @Joel ... Thanks again for all you have shared with me. | |
| Apr 28, 2013 at 11:51 | vote | accept | Rina Shora | ||
| May 2, 2013 at 1:00 | |||||
| Apr 28, 2013 at 11:21 | comment | added | Joel David Hamkins | Unfortunately, I'm unsure about characterizations of the random algebra. | |
| Apr 28, 2013 at 11:02 | comment | added | Rina Shora | Exellent example (consistency in ZFC is enough). What about the second question (random algebra) even when $\kappa$ is the cardinality of continuum ($X=\mathbb{R}$). Is there any characterization. | |
| Apr 28, 2013 at 0:54 | comment | added | Joel David Hamkins | If you don't want to think about forcing, then I suggest the example of the regular open algebra arising from a Suslin line (the existence of such a space is consistent with ZFC, but not provable). This will be c.c.c. and $\omega_1$-dense, but the Boolean algebra is $(\omega,\infty)$-distributive, and so it is not isomorphic to the regular open algebra you suggest for the case of $\kappa=\omega_1$. | |
| Apr 28, 2013 at 0:22 | comment | added | Rina Shora | @Joel , thanks for your reply, very nice examples. Yes both algebras satisfy ccc. Is it possible to find an approach ( to prove it under strong assumption) to Question 1 without forcing methods. I will be pleased to share with me any result you know, or even refer me to the references | |
| Apr 27, 2013 at 21:29 | comment | added | Joel David Hamkins | Meanwhile, there is a characterization of $\operatorname{Add}(\kappa,1)$, which is like $2^\kappa$ but using $\lt\kappa$ support instead of finite support. If that is what you had meant, then I can post something about this. | |
| Apr 27, 2013 at 21:27 | comment | added | Joel David Hamkins | I see now that you didn't actually insist on c.c.c.; but if you drop this, of course there are even more counterexamples. | |
| Apr 27, 2013 at 21:16 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |