Problems

Questions:

(S.V.Sudoplatov) Describe cardinalities λ and forms of approximations for natural classes of theories.

(M.I.Bekenov) Under what conditions does an omega-categorical theory have a (non) smoothly approximable model companion?

(M.I.Bekenov) Under what conditions does a formula-definable (smoothly approximable, pseudofinite theory ) theory have a formula-definable (smoothly approximable, pseudofinite theory )  model companion?

Kueker's conjecture 

Do the Henson graphs have the finite model property?

Is every infinite, minimal field of characteristic zero algebraically closed? (Here, "minimal" means that every definable subset of the structure is finite or co-finite.)