3 problems

Let ${\mathscr{R}}$ be an expansion of $(\mathbb{R},<,+,\times)$, and let ${\mathscr{R}}^\circ$ be its open core. The structure ${\mathscr{R}}$ is type A when it has no dense defin…

Let $\mathbb K$ be a DC structure, and let its open core be the structure whose definable sets are generated by the open definable subsets of $\mathbb K^n$. The i-minimal open-core…

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.