# [FOM] Woodin's pair of articles on CH

Monroe Eskew meskew at math.uci.edu
Sat Jan 16 13:56:16 EST 2010

On Fri, Jan 15, 2010 at 5:26 AM, William Tait <williamtait at mac.com> wrote:
>
> I don't see the problem: interpretations needn't preserve identity.  The identity relation between HC sets becomes an equivalence relation between the well-founded trees. That relation, as I pointed out, is definable in NT^2.
>
> Bill
>

There must be some problem because of the models in which the
proposition fails pointed out by Andreas Blass.

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.