3 problems

Let $X$ be a definable set in the structure $\mathbb R_{\exp}$, and consider the Pila–Wilkie counting function for arithmetic points of bounded height after removing the algebraic…

Let $X\subseteq\mathbb R^n$ be definable in a sharply o-minimal structure with sharp derivatives, and let $k=0,\ldots,n-\dim X-1$. For $g,h\in\mathbb N$, let…

Let $X$ be a set definable in a sharply o-minimal structure, and let $V$ range over algebraic varieties over $mathbb Q$ of dimension $k<\operatorname{codim} X$. Set…