4 problems

Let ${\mathscr{R}}$ be an NIP expansion of $(\mathbb{R},<,+)$ by closed subsets of Euclidean space. A definable set has dimension zero when its dimension in the paper's dimension t…

Let ${\mathscr{R}}$ be an NIP expansion of $(\mathbb{R},<,+)$ by closed subsets of Euclidean space. Call ${\mathscr{R}}$ field-type when it satisfies condition (1): there is a none…

Let ${\mathscr{R}}$ be an expansion of $(\mathbb{R},<,+)$, and let ${\mathscr{R}}^\circ$ denote its open core. The structure $({\mathcal P}(\mathbb{N}),\mathbb{N},\in,s)$ is the tw…

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…