Atomic toposes, choice spectra and model-theoretic stability

For a suitable class of structures $\mathcal{K}$, let ${\rm Sh}(\mathcal{K}_λ^{\rm op},J_{\rm at})$ denote the atomic sheaf topos over the opposite of the category $\mathcal{K}_λ$ of structures in $\mathcal{K}$ of cardinality at most $λ$, with embeddings as morphisms. In this article, we analyze the