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FORKING, IMAGINARIES, AND OTHER FEATURES OF $\text {ACFG}$

Part of: Model theory

Published online by Cambridge University Press:  07 June 2021

CHRISTIAN D’ELBÉE
CHRISTIAN D’ELBÉE*
Affiliation:
EINSTEIN INSTITUTE OF MATHEMATICS THE HEBREW UNIVERSITY OF JERUSALEM GIVAT RAM 9190401, JERUSALEM, ISRAELE-mail:[email protected]:http://choum.net/~chris/page_perso/
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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 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.

Keywords

fields of positive characteristic with generic subgroupNSOP1 theoriesforkingKim-forkingelimination of imaginaries

MSC classification

Primary: 03C10: Quantifier elimination, model completeness and related topics
Secondary: 03C30: Other model constructions 03C45: Classification theory, stability and related concepts 03C65: Models of other mathematical theories
Type
Article
Information
The Journal of Symbolic Logic , Volume 86 , Issue 2 , June 2021 , pp. 669 - 700
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Copyright
© The Association for Symbolic Logic 2021

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