5 problems

Let $\operatorname{\mathcal{K}}$ be an abstract elementary class, let $\operatorname{Hanf}(\operatorname{\mathcal{K}})$ be its Hanf number, and let $LS(\operatorname{\mathcal{K}})$…

EPPA–Ramsey expansion conjecture. Every strong amalgamation class with EPPA has a precompact Ramsey expansion.

Let $T$ be a simple theory and let $3 \leq k \leq \aleph_0$. Consider the following conditions: (A) $T$ has $\mathcal{P}^-(k)$-amalgamation of models; (B) $T$ has $<k$-type amalgam…

Let $\lambda$ be a cardinal. For an abstract elementary class (AEC) $\boldsymbol{K}$, write $\operatorname{LS}(\boldsymbol{K})$ for its Löwenheim–Skolem number, and say that…

A structure is primitive if no nontrivial equivalence relation on its domain is invariant under its automorphism group; it is binary if its language has relation symbols of arity a…