[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
transcendental.)
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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