Forking, Imaginaries and other features of ACFG
Christian d'Elb\'ee

TL;DR
This paper explores the model-theoretic properties of ACFG, an algebraically closed field with an additive subgroup predicate, focusing on imaginaries and independence relations in this non-simple, NSOP1 theory.
Contribution
It provides a detailed analysis of imaginaries and independence relations in ACFG, expanding understanding of its model-theoretic structure.
Findings
Characterization of imaginaries in ACFG
Analysis of Kim-independence and forking independence interactions
Identification of ACFG as an NSOP1 non-simple theory
Abstract
We study the generic theory of algebraically closed fields of fixed positive characteristic with a predicate for an additive subgroup, called . This theory was introduced recently as a new example of non simple theory. In this paper we describe more features of , such as imaginaries. We also study various independence relations in , such as Kim-independence or forking independence, and describe interactions between them.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory · Advanced Topology and Set Theory
