5 problems

Definable-basis conjecture. If $K$ admits a gt-henselian topology with a basis consisting of definable sets, then the $\mathscr{E}_K$-topology is a field topology.

Let $\mathbb{R}_{S_n}$ be the reals at definability level $S_n$, let $\mathbb{R}_{S_\omega}=\bigcup_{n\in\mathbb{N}}\mathbb{R}_{S_n}$, and let $\mathbb{A}_{S_n}$ and…

Let $K$ be a non-big field, meaning an algebraic extension of $\mathbb{Q}$ that is not big, and let $R_K$ denote the ring constructed from the unit group of $K$. Triviality conject…

Recursive definability conjecture. There are formulas $\phi_{n,g}(\vec{x})$, $\psi_{n,g}(\vec{x},\vec{y})$, and $\rho_{n,g}(\vec{x},\vec{z})$, depending recursively on $n$ and $g$,…

Finite-pattern definability conjecture. There is a finite set $\Delta'$ of formulas such that, for every $\phi(x;y)\in p$ and $b,b'\in\mathcal U$, if