FOM: truth and provability

Martin Davis martin at
Tue Nov 7 17:38:27 EST 2000

Can I be the only fom-er getting tired of this discussion going round and 
round in circles?

It likely won't help, but the discussants might want to consider the 
following variant form of Gödel's theorem:

For any consistent axiomatic extension T of Robinson's Q (hence certainly 
PA and ZFC are included) there is a formula with one free variable G(x), 
where numerals representing natural numbers may be substituted for x, such 
1. for each numeral n, G(n) is provable in T.
2. (Ax)G(x) is not provable in T.

And, of course, G(x) can be taken to have a particularly simple arithmetic 
form - supplied on demand.


                           Martin Davis
                    Visiting Scholar UC Berkeley
                      Professor Emeritus, NYU
                          martin at
                          (Add 1 and get 0)

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