FOM: confusion, reply to Friedman

[Colin McLarty]

response to Harvey Friedman  2 Mar 1999 18:12:38

        You cite my claim that this quoted statement

         "If T is a finitely axiomatized fragment of ZFC, then ZFC
        proves Consis(T)".

is expressible but not provable in ZFC. You insist:

>Not only can this quoted assertion be expressed in ZFC, it is actually
>easily proved in ZFC. In fact, it is easily proved within EFA = exponential
>function arithmetic.

I am sure you see there is a universal quantifier over p in the statement
"If a prime p is equal to 1 mod 4, then -1 is a square mod p". In the same
way this quoted statement includes a universal quantifier over T. To be even
more explicit the statement says:

        "For every T, if T is a finitely axiomatized fragment of ZFC, 
        then ZFC proves Consis(T)"

Do you claim this statement is provable in EFA?