Real Algebraic and Analytic Geometry |

A model theoretic application of Gelfond-Schneider theorem.

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Submission: 2008, January 4.

*Abstract:
We prove that weakly o-minimal expansions of the ordered field of
all real algebraic numbers are polynomially bounded.
Apart of this we make a couple of observations concerning weakly o-minimal
expansions of ordered fields of finite transcendence degree
over the rationals. We show for instance that
if Schanuel's conjecture is true and $K\subseteq\mathbb{R}$ is a
field of finite transcendence degree over the rationals, then
weakly o-minimal expansions of $(K,\leq,+,\cdot)$ are polynomially bounded.*

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