Timeline for continuum many mutually generic filters
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 1, 2014 at 21:52 | comment | added | Monroe Eskew | Oh I see, it's only when you have a pair of incompatible elements that you extend to a pair in $E_n$. | |
| Aug 1, 2014 at 21:30 | comment | added | Andreas Blass | @MonroeEskew Yes, I intended "dense open" and I actually wrote that in the sentence about infinite repetition, but I neglected to do so when first introducing the $E_n$'s. About your second observation: I think some more work would be needed to avoid the infinite repetition. The problem is that you could have $r\neq r'$ yet $r\upharpoonright n=r'\upharpoonright n$ for a particular $n$. The infinite repetition ensures that $E_n$ will be treated again, for larger values of $n$, where this problem no longer occurs. | |
| Aug 1, 2014 at 21:27 | vote | accept | Monroe Eskew | ||
| Aug 1, 2014 at 21:25 | comment | added | Monroe Eskew | Very nice, thanks. 2 minor remarks. It seems clearer if the $E_n$'s are dense open. Also, I don't see why you need to repeat them infinitely often. For any $n$, $(p_{r \restriction n}, p_{r' \restriction n}) \in E_n \cap G \times G'$, showing mutual genericity because $n$ is arbitrary, right? | |
| Aug 1, 2014 at 21:06 | history | answered | Andreas Blass | CC BY-SA 3.0 |