3 problems

Let $X$ be a variety in characteristic $0$. The uniruledness and Iitaka-fibration conjecture. Either $X$ is uniruled, or $\operatorname{Kod}(X)\geq 0$. If…

Bigstar property conjecture. There is a classification-theoretic property $\bigstar$ such that: (1) there is a property $P$ of set systems for which $T$ has $\bigstar$ if and only…

Dichotomy conjecture. There is a dichotomy: either the model is similar to categorical theories, or there are “many complicated models”.