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

Akash Hossain
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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.
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阿贝尔群纯短精确序列展开中分叉和分割的转移原理
阿申布伦纳、切尔尼科夫、盖雷特和齐格勒在他们关于有价域的远度的文章中,证明了阿贝尔结构纯短精确序列中量化消除的辉煌的阿克斯-科钦-厄尔肖夫原理。韦斯特研究了他们的工作与分叉的关系,我们证明了在这种情况下分叉和分割的阿克斯-科钦-厄尔肖夫原理。
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