Schanuel's Conjecture
Let 
, ..., 
be linearly independent over the Rationals 
,then
has Transcendence degree at least
over . Schanuel's conjecture is ageneralization of the Lindemann-Weierstraß Theorem. If the conjecture is true,then it follows that 
and 
are algebraically independent. Mcintyre (1991) proved that the truth of Schanuel'sconjecture also guarantees that there are no unexpected exponential-algebraic relations on the Integers
(Marker 1996).See also Constant Problem
References
Macintyre, A. ``Schanuel's Conjecture and Free Exponential Rings.'' Ann. Pure Appl. Logic 51, 241-246, 1991. Marker, D. ``Model Theory and Exponentiation.'' Not. Amer. Math. Soc. 43, 753-759, 1996.
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