[FOM] logical complexity of mathematical statements

[Harvey Friedman]

Effectively computable is nice but extremely weak. What more does it
give? Say a small finite exponential stack?

Harvey

On Tue, Oct 13, 2015 at 4:18 PM, Timothy Y. Chow <tchow at alum.mit.edu> wrote:
> Harvey Friedman wrote:
>
>> "Linearly independent logarithms of algebraic numbers are
>> algebraically independent" by similar reasoning seems to be Pi03. Look
>> at Baker's Theorem, a special case. Does Baker give a bound for the
>> corresponding Pi03 statement, and if so, what kind of bound?
>
>
> Yes, if L_1, ..., L_n are the linearly independent logarithms of algebraic
> numbers and a_0, ..., a_n are algebraic numbers (not all zero) then Baker
> gives an effectively computable nonzero lower bound for
>
>   | a_0 + a_1 L_1 + ... + a_n L_n |