The plan for last semester was to finish a chapter in choiceless higher Chang conjectures. There was a change of plans when (luckily) Arthur Apter asked me to give a talk explaining the construction in Gitik's "All uncountable cardinals can be singular". Trying to simplify the construction I was busy with it all semester. I managed to simplify it only a little bit, in that requirement (4) in the definition of P2 wasn't really necessary and the proof of ZFC-powerset in the generic extension is replaced by a proof that the forcing is pretame. Moreover now the construction is more susceptible to modifications. This together with some applications of this construction are going to be part of my upcoming PhD thesis. Recent estimates for my graduation are April to May 2009.
Right now I'm finally finishing up the chapter on the higher Chang conjectures. I will give a talk about that in the Colloquium Logicum 2008, next week in Darmstadt. Also, it turns out that Gitik's "everything singular"-method had something to say about these Chang conjectures too. What a great construction!
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