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FORKING, IMAGINARIES, AND OTHER FEATURES OF
$\text {ACFG}$
- Part of
-
- Journal:
- The Journal of Symbolic Logic / Volume 86 / Issue 2 / June 2021
- Published online by Cambridge University Press:
- 07 June 2021, pp. 669-700
- Print publication:
- June 2021
-
- Article
- Export citation
-
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 in [16] as a new example of 
$\mathrm {NSOP}_{1}$
nonsimple 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.
