Jerusalem, we (may?) have a problem

June 2, 2011 at 15:35 | Posted in Uncategorized | Leave a comment

Having spent most of my professional career wrestling with papers of Shelah, I’ve come to know quite well that special sinking feeling when one comes across the word “straightforward” in a situation where the hypotheses needed don’t appear to be satisfied. Looking to the end of his proof of Lemma 3.5 on page 383 of Cardinal Arithmetic, I can already see there’s a problem, and I worry that the problem is a serious one, as the construction given doesn’t on the face of it arrange for the hypotheses of Claim 3.3A to hold, at least not in a manner that is in any sense straightforward. What worries me is that this is a situation close to something we looked at in the first project, and we know that lots of what was originally claimed in the first section of [Sh:430] was retracted.

Anyway, I think I’ll keep this project going and establish what I’m able to establish by these techniques. At the very least, I want to be able to pin down exactly where the problem lies. Maybe I’ll figure out what he means by “straightforward”, but if I don’t I’ll probably end up looking at his original proof of the cov vs. pp theorem and see what I can make of it.

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