4 problems

Let $G$ be an ordered abelian group. Distal expansion conjecture. Every ordered abelian group admits a distal expansion. This proposes that distality can always be obtained by expa…

Let $(R,<,+)$ be a dense archimedean ordered abelian group, let ${\mathscr{R}}$ be a strongly dependent and noiseless expansion, and let ${\mathscr{N}}$ be a highly saturated eleme…

Let $(R,<,+)$ be a dense archimedean ordered abelian group, let ${\mathscr{R}}$ be an expansion of it, and let ${\mathscr{R}}^{\square}$ be the completion structure used in the pap…

Non-definability conjecture. In no nontrivial precontraction group $(\Gamma,\chi)$ can one define, even allowing parameters, a function $\psi:\Gamma^{\neq}\to\Gamma$ such that…