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Recently Moti Gitik has refuted Shelah's PCF conjecture (see Short extenders forcings II ) by proving the following theorem:

Theorem. Assuming the consistency of infinitely many strong cardinals, one can force a countable set of successor cardinals $A$ such that $|PCF(A)|=\aleph_1$.

I wonder to know if anyone can explain the main ideas behind Gitik's proof of the above theorem.

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    $\begingroup$ I bet Moti could. :-) $\endgroup$
    – Asaf Karagila ♦
    Commented Aug 19, 2014 at 4:37
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    $\begingroup$ I asked this question of many people at Oberwolfach. The answers were the same as Asaf's comment. ;) $\endgroup$
    – Todd Eisworth
    Commented Aug 19, 2014 at 15:31
  • $\begingroup$ Mohammad, @Todd, Moti has began giving an informal course about his proof, and I'm Live-TeXing the whole thing. When there's something to post, I'll probably post it on my site and/or include an answer here if I can give one. He tried to give some approximate idea today, but I drifted off since he started drawing all these diagrams on cardinal structure and whatnot. But speaking to others, it didn't come across very well, and will probably clarify over the next couple of weeks. $\endgroup$
    – Asaf Karagila ♦
    Commented Nov 12, 2014 at 19:20
  • $\begingroup$ Good luck with this! This proof is one that needs to be clarified and assimilated ASAP, because it opens up so many possibilities to answer open questions. $\endgroup$
    – Todd Eisworth
    Commented Nov 12, 2014 at 19:25
  • $\begingroup$ @Todd: Today was the first lecture, and the crowd was roughly 20 people. Surely if I won't be the one to understand it, clear it up and explain it better, someone much better than me at these things will do it. $\endgroup$
    – Asaf Karagila ♦
    Commented Nov 12, 2014 at 21:02

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