5 problems

NIP group conjecture. If $\mathscr{M}$ is $\aleph_0$-categorical and NIP, then $\mathscr{M}$ interprets an infinite group if and only if $\mathscr{M}$ trace defines an infinite gro…

Finite-arity conjecture. For every $d\in\mathbb{N}_{\ge 1}$, there are only finitely many $d$-ary finitely homogeneous structures modulo trace equivalence.

Binary trace-equivalence conjecture. Every structure admitting quantifier elimination in a finite binary relational language is trace equivalent to either the trivial structure,…

Countability and finite arity conjecture. There are only countably many finitely homogeneous structures modulo trace equivalence. More strongly, for every $k65 1$ there are only fi…

Ordered-abelian-group conjecture. An ordered abelian group cannot trace define an infinite field.