We prove the following theorem: let $\widetilde{\mathcal R}$ be an expansion of the real field $\overline{\mathbb R}$, such that every definable set (I) is a uniform countable union of semialgebraic sets, and (II) contains a "semialgebraic chunk". Then every definable smooth function $f:X\subseteq \mathbb R^n\to \mathbb R$ with open semialgebraic domain is semialgebraic... (read more)

PDF Abstract- LOGIC