Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

The following concept is due to Shelah and I have some issues with a claim using this notion: Suppose that $\nu$ is a limit ordinal and that $P_\nu$ is an iteration of forcing notions. We say that a $P_\nu$ name $\dot{\alpha}$ of an ordinal is $prompt$ iff the following two things hold:

  1. $\Vdash_\nu \dot{\alpha} \le \nu$

  2. If $p \Vdash_\nu "\dot{\alpha} = \xi"$ then even $p \upharpoonright \xi ^\smallfrown 1_\nu \upharpoonright [\xi, \nu) \Vdash_\nu \dot{\alpha} = \xi$ ( $1_\nu$ should be the largest element of the iteration, and $\xi$ is the hacek name of an ordinal though I refused to write the hacek)

Then the following two things should hold:

  1. If $\dot{\alpha}$ is prompt $\eta \le \nu$ and if $p \Vdash_\nu \eta \le \dot{\alpha}$ then $p \upharpoonright \xi ^\smallfrown 1_\nu \upharpoonright [\xi, \nu) \Vdash_\nu \eta \le \dot{\alpha}$
  2. If $\dot{\alpha_i}$ are prompt then so is the supremum $sup$ and the minimum $min$

I have problems proving those two assertions so any help would be highly appreciated. Thank you!

share|cite|improve this question

closed as too localized by Asaf Karagila, Amzoti, Chris Godsil, Henry T. Horton, J. M. Jun 1 '13 at 5:39

This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

By $p|\xi\frown 1_\nu | [\xi,\nu)$ you mean the condition $q$ which agrees with $p$ up to $\xi$ and it has constant value the largest element after $\xi$. – azarel Feb 8 '12 at 18:01
I would suggest that nontrivial questions about forcing are better placed on mathoverflow. (And this would seem especially true for questions about iterated forcing.) – JDH Feb 8 '12 at 19:37
It was suggested in a moderator flag that this question be migrated to MathOverflow. Just wanted to explain that MathOverflow is not a part of the SE 2.0 network (or at least, not yet), so question migration is not possible - it would have to be reposted by hand. – Zev Chonoles Feb 9 '12 at 7:31
Ok, its now posted on MO – Stefan Hoffelner Feb 9 '12 at 10:09
Posted on MO:… – Asaf Karagila Feb 9 '12 at 10:26