4 problems

Let $\omega$ be a definable modulus of continuity, let $X\subseteq\mathbb{R}^n$ be a closed definable set, and let $f$ belong to the trace space…

Convergence conjecture. Beyond subsequential convergence, the iterates $(w_k)_{k\in\mathbb{N}}$ should converge when $\mathcal{J}$ is definable.

Let $(\mathbb{Q},<,+,0)$ be expanded to an o-minimal structure, and let $f\colon\mathbb{Q}\to\mathbb{Q}$ be definable. Eventual rational-linearity conjecture. The function $f$ is e…

The structures under consideration have restricted multiplication and no definable addition, while definable Skolem functions mean definable choices of points in the fibers of defi…