FOM: truth and provability
Martin Davis
martin at eipye.com
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
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
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