[FOM] Is Gelfond-Schneider constructive?

Andrew Aberdein aberdein at fit.edu
Tue Mar 8 20:52:06 EST 2005

Can anyone tell me if there is a constructive proof of the 
Gelfond-Schneider theorem?  (The theorem that if a  is algebraic (and 
neither 0 or 1) and b is irrational algebraic, then a^b is 

Anne Troelstra implies that there is:

p.9 of turing.wins.uva.nl/~anne/eolss.pdf

I should have been inclined to take his word for it, if it weren't that 
Jonathan Borwein says that there isn't:

p. 16 of www.cecm.sfu.ca/personal/jborwein/virtual.pdf

and Pawel Urzyczyn & M.H. Sorensen state that the only proofs they've 
seen are non-constructive:

p. 49 of www.mimuw.edu.pl/~urzy/Int/rozdzial2.ps

Can anyone help to resolve my confusion?

Regards, Andrew Aberdein

A n d r e w   A b e r d e i n,  P h. D.
Humanities and Communication,
Florida Institute of Technology,
Melbourne, Florida 32901-6975, U.S.A.
[+1] (321) 674 8368   http://www.fit.edu/~aberdein/

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