8 problems

Let a strongly minimal structure be a structure in which every definable subset of its universe is finite or cofinite, and let a structure be non-locally modular when it is not loc…

Let $\mathcal R$ be an o-minimal expansion of a real closed field, and let $\mathcal M$ be a non-locally modular strongly minimal $\mathcal R$-relic, meaning a strongly minimal str…

Let $\mathbb K$ and $\mathcal K$ be the ambient field and structure, and let $N$ be a $\mathbb K$-definable set of dimension one. Let $\mathcal N=(N,\ldots)$ be a strongly minimal,…

Let ${\mathcal M}$ be an o-minimal structure and ${\mathcal D}$ a strongly minimal structure whose underlying set and atomic relations are definable in ${\mathcal M}$. The o-minima…

The trichotomy conjecture. For every strongly minimal structure ${\bf M}$, its geometry is either locally modular, or is the same as the geometry of an algebraically closed field;…

A strongly minimal structure is a first-order structure in which every definable subset of every one-dimensional definable set is finite or cofinite. Zilber's conjecture. A strongl…

Valued-field version of Peterzil's conjecture. Then $M$ interprets a field.

Zilber's conjecture. If $M$ is not locally modular, then $M$ interprets a field.