[FOM] obscure technical question concerning ZF without choice

Harvey Friedman friedman at math.ohio-state.edu
Wed Jan 28 04:48:54 EST 2009

In the plan I sketch in http://www.cs.nyu.edu/pipermail/fom/2009-January/013339.html
I indicated a plan for how the hierarchy can be made long for  
countable sets of subsets of omega. Then I said that this should be  
done for all countable sets of subsets of infinite successor  
cardinals, also.

I neglected to say that when doing this for subsets of kappa^+, we  
need to force not with finite conditions, but conditions of  
cardinality <= kappa. This is so that the different forcings for the  
various kappa^+ can be combined into one construction in a way that  
doesn't interfere with each other - a method originated, I believe, by  
Easton in the early days of forcing.

Harvey Friedman

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