2 problems

Let $T$ be an elementary first-order theory, and consider its countable models up to isomorphism. Vaught's conjecture. The number of countable models of $T$ is either countable or…

Let $\mathfrak A$ be an age in a finite relational language, and let $\operatorname{Mod}(\mathfrak A)/{\equiv}$ denote the bi-embeddability classes of countable structures with age…