10 problems

Let $F$ be a strongly NIP ordered field. Such a field is almost real closed if it admits a henselian valuation whose residue field is real closed. Shelah–Hasson conjecture for orde…

Archimedean specialization of Shelah's conjecture. Then $K$ is real closed.

Classification conjecture. Any strongly NIP ordered field $(K,<)$ is almost real closed.

Let $\mathbb{L}$ be the class of log-atomic surreal numbers, and let $\mathbb{R}\langle\langle\mathbb{L}\rangle\rangle$ denote the associated field of exponential-logarithmic trans…

Let $\mathbb{K}$ be a definably complete expansion of an ordered field, and let $f:[0,1]^2\to[0,1]^2$ be a definable continuous function. Then Brower's fixed-point conjecture. Ther…

Let $\mathbb{K}$ be an expansion of an ordered field, let $D \subseteq K_{\geq 0}$ be a definable closed discrete subset, let $h:D\to K_{\geq 0}$ be definable, and let…

Let $\mathbb{K}$ be a definably complete expansion of an ordered field, and let $\mu$ be the outer measure defined by infima of sums of lengths of definable open-interval covers in…

Let $d\ge2$. Write $\operatorname{Num}(\mathsf{Th})$ for the class of quantity structures of models of a theory $\mathsf{Th}$, and let $\mathsf{SpecRel}_d$ be the axiom system for…

A restrained structure is a DC expansion of an ordered field such that, for every definable discrete set $D \subseteq \mathbb K^n$ and every definable function $g:D\to\mathbb K$, t…

Let $F$ be an ordered field and $I$ an integer part for $F$. The structure $angle F,Iangle$ is separable if it satisfies the separability property: for all real numbers…