Timeline for Gluing functions together in the generic extension
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 6, 2011 at 18:51 | vote | accept | Stefan Hoffelner | ||
| Apr 6, 2011 at 18:03 | answer | added | Andreas Blass | timeline score: 2 | |
| Apr 6, 2011 at 17:17 | comment | added | Justin Palumbo | (by the way this argument has almost nothing to do with random forcing, and will work for essentially any A and I) | |
| Apr 6, 2011 at 17:06 | comment | added | Justin Palumbo | Take $A$ to be $2^\omega$, and let $I$ be the ideal of all measure zero sets. This is random forcing. Let $X$ be the collection of all members of $2^\omega$ whose first digit is 0, and $Y$ be all those whose first digit is 1. Exactly one of these lie in any generic filter $G$. Let $\dot{f}$ name the function which is constantly 0 if $G$ contains $X$, and constantly 1 if $G$ contains $Y$. Then $X$ and $Y$ together form a maximal antichain, but if you do the gluing process you describe, you get a function which is 0 on $X$ and 1 on $Y$, and so cannot equal $\dot{f}$, whatever it ends up being. | |
| Apr 6, 2011 at 16:49 | comment | added | Stefan Hoffelner | If you're right, Justin then this would explain why I had a hard time proving it. The above 'gluing fact' seems to appear in a lemma in the lecture of my professor, and no one of the sophisticated audience said anything against it. However Jech's book (currently my only source of knowledge at hand) has to say very little about Random Forcing, so I would be glad if you could explain your comment a little bit. | |
| Apr 6, 2011 at 15:57 | comment | added | Justin Palumbo | I don't think your gluing fact is true in the generality you've given. For example, do random forcing and take $\dot{f}$ to name the function which is constantly whatever value the adjoined random real takes at 0. Gluing will net you a $g$ which isn't a constant function. | |
| Apr 6, 2011 at 15:03 | history | asked | Stefan Hoffelner | CC BY-SA 2.5 |