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

TL;DR

This paper extends Ax-Kochen-Ershov principles to forking and dividing in pure short exact sequences of Abelian groups, advancing model-theoretic understanding of these algebraic structures.

Contribution

It introduces transfer principles for forking and dividing in expansions of pure short exact sequences of Abelian groups, building on prior work on quantifier elimination.

Findings

Established Ax-Kochen-Ershov principles for forking.

Connected forking behavior to existing quantifier elimination results.

Enhanced understanding of model-theoretic properties of Abelian group sequences.

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.