[FOM] Logically Natural Examples 1

Ali Enayat ali.enayat at gmail.com
Thu Dec 21 14:49:20 EST 2017

This is a small comment on Harvey Friedman's recent posting (Dec 21, 2017),
in which he quoted the following theorem as follows:

> THEOREM (Cohen)? Assume ZFC is consistent. There is no formula phi(x)
> in the language of set theory, with only the free variable x, such
> that ZFC proves that the unique solution to phi(x) is a well ordering
> of R.

The point of this posting is that the above theorem is due to Solomon
Feferman, and first appeared in the following landmark paper of his, which
also includes -- for the first time -- various applications of forcing to
the arithmetical context:

Some applications of the notions of forcing and generic sets.
Fund. Math. 56 1964/1965 325–345.

(available via http://matwbn.icm.edu.pl/ksiazki/fm/fm56/fm56129.pdf)

Best regards,

Ali Enayat
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