Real Algebraic and Analytic Geometry Preprint Server

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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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