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Forking and Dividing in NTP2 theories

Published online by Cambridge University Press:  12 March 2014

Artem Chernikov  and
Itay Kaplan
Artem Chernikov
Affiliation:
Université Lyon 1, CNRS, Institut Camille Jordan UMR5208, 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne Cedex, France, E-mail: artyom.chernikov@gmail.com
Itay Kaplan*
Affiliation:
Fachbereich Mathematik und Statistik, Universität Konstanz, 78457 Konstanz, Germany
*
Mathematisches Institut und Institut für Mathematische Logik und Grundlagenforschung Fachbereich Mathematik und Informatik, Universität Münster, Einsteinstrasse 62, 48149 Münster, Germany, E-mail: itay.kaplan@uni-konstanz.de
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Abstract

We prove that in theories without the tree property of the second kind (which include dependent and simple theories) forking and dividing over models are the same, and in fact over any extension base. As an application we show that dependence is equivalent to bounded non-forking assuming NTP2.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 1 , March 2012 , pp. 1 - 20
Copyright
Copyright © Association for Symbolic Logic 2012

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References

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