[FOM] Woodin's pair of articles on CH

T.Forster@dpmms.cam.ac.uk T.Forster at dpmms.cam.ac.uk
Sun Jan 17 16:03:15 EST 2010

On Jan 17 2010, Monroe Eskew wrote:

>I apologize-- the point below is not relevant.  In ZFC we could do the
>proof using these equivalence classes to count things instead of
>choosing representatives.  I think the step that requires choice is
>just that old proposition saying that a \kappa sized union of sets
>each of size less than \kappa is size (at most) \kappa.

You need choice to pick, for each countable set, one of the wellordings of 
it to length omega. I'm not sure that's the same; it may be stronger

>On Sat, Jan 16, 2010 at 10:56 AM, Monroe Eskew <meskew at math.uci.edu> wrote:
>> Mapping to the equivalence class of well founded partial orders on
>> omega avoids choice at that step.  But the equivalence classes are not
>> in H_{\omega_1} since they are of size continuum.
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