Forking, Imaginaries and other features of ACFG

Christian d'Elbée

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arXiv · 1812.09378

Forking, Imaginaries and other features of ACFG

Christian d'Elbée

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Abstract

We study the generic theory of algebraically closed fields of fixed positive characteristic with a predicate for an additive subgroup, called $\mathrm{ACFG}$. This theory was introduced recently as a new example of $\mathrm{NSOP}_1$ non simple theory. In this paper we describe more features of $\mathrm{ACFG}$, such as imaginaries. We also study various independence relations in $\mathrm{ACFG}$, such as Kim-independence or forking independence, and describe interactions between them.

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Christian d'Elbée. 2018-12-21. Forking, Imaginaries and other features of ACFG. https://arxiv.org/abs/1812.09378

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