In the $(*)$ below, I would like to understand whether "all we have to do is find $q>p$ such that ..." or as I would say $q\geq p$ such that...
I have two questions about this: does this make any difference whether we are looking for such $q>p$ or $q\geq p$ and whether we can w.l.o.g. look for $q\geq p$. Please note the opposite notion of stronger than in Shelah conception of forcing.
