[FOM] Woodin's pair of articles on CH

T.Forster@dpmms.cam.ac.uk T.Forster at dpmms.cam.ac.uk
Tue Jan 19 02:20:17 EST 2010

this looks like *exacrtly* what i wanted to know.

On Jan 18 2010, Ali Enayat wrote:

>This note is in response to the recent discussion about Woodin's
>reference to the well-known fact that the standard model for second
>order number theory is "essentially the same" as the model
>(M,epsilon), where M is the set of hereditarily countable sets.
>As suggested out by Bill Tait, the above two structures are intimately
>related at the interpretability level, i.e., they are
>*bi-interpretable* . Note that this is stronger than saying that they
>are mutually interpretable, e.g. the two theories ZF and ZFC are
>mutually interpretable, but they are not bi-interpretable since, by an
>old result of Cohen, ZF has a model with an automorphism of order 2,
>but as noted by Harvey Friedman, ZFC cannot have such a model

Can you supply a definition of *bi-interpretable*? I can see why ZF with 
foundation connot have any automorphisms, but i don't see what AC has to do 
with it

>[By the way, I highly recommend Friedman's paper INTERPRETATIONS,
>ACCORDING TO TARSKI for a quick but deep introductionto the subject].

Have you got a reference or a URL?

The rest of your post suggests i should swell Steve royalties by buying his 
book. Well it's probably about time!


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