[FOM] Woodin's pair of articles on CH

[Monroe Eskew]

On Tue, Jan 12, 2010 at 3:29 PM, William Tait <williamtait at mac.com> wrote:
>In the other direction, a hereditarily countable set can be coded (not necessarily uniquely) by a well-founded tree whose nodes >are natural numbers, which in turn can be coded by a set of natural numbers.  The relation between two trees representing the >same hereditarily countable set is definable in NT^2.

The problem is the "not necessarily uniquely" clause.  To produce the
desired injection,  AC must be used to choose a tree relation on the
naturals for each countable transitive set.

-Monroe