Transfer principles for forking and dividing in expansions of pure short exact sequences of Abelian groups

Abstract

In their article about distality in valued fields, Aschenbrenner, Chernikov, Gehret and Ziegler proved resplendent Ax-Kochen-Ershov principles for quantifier elimination in pure short exact sequences of Abelian structures. We study how their work relates to forking, and we prove Ax-Kochen-Ershov principles for forking and dividing in this setting.