3 problems

Main conjecture on expansions of the real field. An expansion of $(\mathbb{R},+,\cdot)$ by constructible sets defines a dense and codense subset of $\mathbb{R}$ if and only if it d…

Let $P$ and $Q$ be polynomial functors over $\mathbb{R}$, let $Y\subseteq Q$ be a semialgebraic subset, and let $\alpha:Q\to P$ be a polynomial transformation. Write…

Let $F_A$ denote the class of maps associated with a matrix $A$, and let a matrix be called proper when the corresponding map $F_A$ is proper. Conjecture C. The set of matrices $A$…