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Stable types in rosy theories

Published online by Cambridge University Press:  12 March 2014

Assaf Hasson  and
Alf Onshuus
Assaf Hasson*
Affiliation:
Mathematical Institute, Oxford University, Oxford, UK
Alf Onshuus
Affiliation:
Universidad de Los Andes, Departamento de Matemáticas, CRA. 1 No 18A-10, Bogotá, Colombia. E-mail: aonshuus@uniandes.edu.co, URL: http://matematicas.uniandes.edu.co/cv/webpage.php?Uid=aonshuus
*
Department of Mathematics, Ben Gurion University of the Negev, Be'er Sheva, Israel. E-mail: hassonas@.math.bgu.ac.il
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Abstract

We study the behaviour of stable types in rosy theories. The main technical result is that a non-þ-forking extension of an unstable type is unstable. We apply this to show that a rosy group with a þ-generic stable type is stable. In the context of super-rosy theories of finite rank we conclude that non-trivial stable types of Uþ-rank 1 must arise from definable stable sets.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 4 , December 2010 , pp. 1211 - 1230
Copyright
Copyright © Association for Symbolic Logic 2010

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