FOM: truth and provability

[Martin Davis]

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 
that:
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




                           Martin Davis
                    Visiting Scholar UC Berkeley
                      Professor Emeritus, NYU
                          martin at eipye.com
                          (Add 1 and get 0)
                        http://www.eipye.com