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STABILIZERS, $\text{NTP}_{2}$ GROUPS WITH $\text{f}$-GENERICS, AND PRC FIELDS

Part of: Model theory

Published online by Cambridge University Press:  10 May 2018

Samaria Montenegro ,
Alf Onshuus  and
Pierre Simon
Samaria Montenegro
Affiliation:
Escuela de Matemática-CIMPA, Universidad de Costa Rica, San José, Costa Rica ([email protected]) Departamento de Matemáticas, Universidad de los Andes, Bogotá, Colombia ([email protected])
Alf Onshuus
Affiliation:
Departamento de Matemáticas, Universidad de los Andes, Bogotá, Colombia ([email protected])
Pierre Simon
Affiliation:
Department of Mathematics, University of California, Berkeley, CA, USA ([email protected])
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Abstract

In this paper, we develop three different subjects. We study and prove alternative versions of Hrushovski’s ‘stabilizer theorem’, we generalize part of the basic theory of definably amenable NIP groups to $\text{NTP}_{2}$ theories, and finally, we use all this machinery to study groups with f-generic types definable in bounded pseudo real closed fields.

Keywords

model theoryPRCf-genericsdefinable groupsNIPNTP2

MSC classification

Primary: 03C45: Classification theory, stability and related concepts 03C60: Model-theoretic algebra
Secondary: 03C98: Applications of model theory
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 19 , Issue 3 , May 2020 , pp. 821 - 853
Copyright
© Cambridge University Press 2018

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Footnotes

The first and second authors were partially supported by Colciencias grant number 120471250707. The third author was partially supported by ValCoMo (ANR-13-BS01-0006), NSF (grant DMS 1665491), and the Sloan foundation.

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