The paper on pseudofinite abelian groups studies which infinite abelian groups can be viewed as ultraproducts of finite abelian groups, meaning they share all first-order properties with some family of finite groups. A natural but unresolved problem is whether one can write down a complete and explicit set of axioms for such groups that simultaneously encodes not just the logical truth values of sentences but also the asymptotic proportions of solutions to those sentences inside the finite approximating groups. In other words, can the full quantitative shadow of finiteness, not just its qualitative echo, be axiomatized in a tractable logical framework?