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.
- Peg Knot
- Peg Solitaire
- Peg Top
- Peirce's Theorem
- p-Element
- Pell Equation
- Pell-Lucas Number
- Pell-Lucas Polynomial
- Pell Number
- Pell Polynomial
- Pell Sequence
- Pencil
- Penrose Stairway
- Penrose Tiles
- Penrose Triangle
- Penrose Tribar
- Pentabolo
- Pentacle
- Pentacontagon
- Pentad
- Pentadecagon
- Pentaflake
- Pentagon
- Pentagonal Antiprism
- Pentagonal Cupola