Timeline for Function Approximation in c.c.c Forcings without AC in Ground Model
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 2, 2014 at 19:12 | comment | added | Andreas Blass | @AsafKaragila Right; Ccc for a poset is, as far as I can see, weaker than ccc for its Boolean completion. | |
| Mar 2, 2014 at 15:24 | history | edited | Asaf Karagila♦ | CC BY-SA 3.0 |
added 185 characters in body
|
| Mar 2, 2014 at 15:19 | comment | added | Asaf Karagila♦ | @Andreas: Oh yeah, you're absolutely right there. Generally, though, if $P$ satisfies c.c.c., it doesn't imply that $B(P)$, its Boolean completion, satisfies c.c.c. as well, right? | |
| Mar 2, 2014 at 15:15 | comment | added | Andreas Blass | Concerning the complete Boolean algebra case in the last paragraph of your answer, the situation is even better. If $P$ is a complete Boolean algebra and satisfies the c.c.c., then $F(a)$ will be countable because the truth values $\Vert \dot f(\check a)=\check b\Vert$ constitute an antichain. | |
| Mar 2, 2014 at 15:10 | comment | added | Andreas Blass | I'm also accustomed to calling it the maximality principle. | |
| Mar 2, 2014 at 12:41 | comment | added | Asaf Karagila♦ | Also, Joel, Arnie Miller calls this "the maximum principle", math.wisc.edu/~miller/res/max.pdf | |
| Mar 2, 2014 at 12:41 | comment | added | Asaf Karagila♦ | Joel, I believe that you might be right. And I also believe this is the $\omega_1$-th time that you mentioned that. But since this is in fact the $\omega_1$-th time, it doesn't seem to be catching on in my brain. | |
| Mar 2, 2014 at 12:32 | comment | added | Joel David Hamkins | I believe that what you call the maximality principle is more commonly known as fullness. | |
| Mar 2, 2014 at 12:26 | history | answered | Asaf Karagila♦ | CC BY-SA 3.0 |