4 problems

Let $G$ be a closed oligomorphic permutation group, meaning a closed permutation group with finitely many orbits on $n$-tuples for every $n\geq 1$. An expansion of an $\omega$-cate…

Ramsey-ordering conjecture. There exists such a Ramsey ordering for which, for all $\beta,\beta'\in\mathcal{B}$ and $\gamma,\gamma'\in\mathcal{C}$,

Bodirsky–Schneider–Thom conjecture. If $G\curvearrowright\Omega$ is oligomorphic, then all mixed identities of $G$ are singular.

Let $G$ be a primitive oligomorphic permutation group acting on a countable infinite set … of size $n$. Macpherson's theorem states that there is a constant $c>1$ such that either…