6 problems

Let $\mathbb{K}$ be a d-minimal structure, let $p \in \mathbb{N}$, and let $\mathcal A$ be a finite collection of definable subsets of $\mathbb{K}^n$. A definable $\mathcal C^p$-su…

Let $\mathcal R$ be a d-minimal expansion of $\bar{\mathbb{R}}$. Let $X \subseteq \mathbb{R}^n$ be a manifold definable in $\mathcal R$, and let $Y \subseteq X$ be clopen in $X$. C…

Let $\mathbb{K}$ be a structure in the setting of the paper, and let $X \subseteq \mathbb{K}^n$ be definable and closed. Definable Baire conjecture. The set $X$ is definably Baire.…

Let $\mathcal R$ be a d-minimal expansion of $\overline{\mathbb{R}}$. Let $X\subseteq\mathbb{R}^n$ be a manifold definable in $\mathcal R$, and let $Y\subseteq X$ be clopen in $X$.…

The torsion conjecture. For every $1\leq n\in\mathbb{N}$,

D-minimal open-core conjecture. For every $n\in\mathbb{N}$, every $\mathcal F_\sigma$ subset of $\mathbb{K}^n$ is constructible. Moreover, $\mathbb{K}$ is Baire.