4 problems

Zilber's conjecture. Non-local modularity is necessary and sufficient for a reduct of $(\mathbb C; +,\times)$ to define an isomorphic copy of $(\mathbb C; +,\times)$.

Finiteness conjecture. There are only finitely many first-order reducts of $\mathcal{A}$ up to interdefinability.

Let $T$ be a countable, complete theory that is not small, meaning that for some $k$ there are uncountably many $k$-types. Borel-complete reduct conjecture. Some model of $T$ has a…

A countable homogeneous structure is a countable structure in a finite relational language in which every isomorphism between finite substructures extends to an automorphism. Two r…