Medium Term GoalsMarch 6, 2012 at 11:35 | Posted in Uncategorized | Leave a comment
I feel the urge to return to the main work of this blog, namely working through the details of the more exotic portions of “The Book” and its continuations. I also happen to have an ideal body of results to attack:
As noted earlier, Shelah’s second proof of the “cov vs. pp Theorem” ([Sh:400] 3.5) contains an error (acknowledged in [Sh:513]), and although it is possible to effect a repair of most of it, the full version is still unproven. Now if we look ahead to [Sh:410] (one of the first papers continuing The Book) we find that a great many proofs of theorems end with a sentence saying roughly “now repeat the proof of [Sh:400, 3.5]” (I count at least four instances of this in Section 2 of the paper).
So on the face of it, it’s not clear how many of these results are actually valid. It may be that the weaker version of [Sh:400, 3.5] is strong enough to push through the arguments, but since there are very few details it’s hard to tell.
This looks like a nice task for me to tackle in the blog, so that’s probably what I will do.