[FOM] Woodin's pair of articles on CH
Monroe Eskew
meskew at math.uci.edu
Thu Jan 14 01:11:34 EST 2010
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
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