[FOM] Absolute undecidability

[Timothy Y. Chow]

Harvey Friedman asks for a reference for the irrationality measure of pi. 
I had in mind Salikhov, Russian Mathematical Surveys (2008), 63(3):570.

As Harvey suspects, results of this type are usually ineffective.  I don't 
think that there is much hope of proving that they are "necessarily" 
ineffective, though, because there do exist effective results in this 
subject.  In particular, people have proven effective irrationality 
measures for some numbers, though not (to my knowledge) the most glamorous 
ones such as pi.

Tim