The Journal of Symbolic Logic

Research Article

Stable types in rosy theories

Assaf Hassona1 c1 * and Alf Onshuusa2

a1 Mathematical Institute, Oxford University, Oxford, UK

a2 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

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.

(Received October 26 2008)

Correspondence

c1 Department of Mathematics, Ben Gurion University of the Negev, Be'er Sheva, Israel. E-mail: hassonas@.math.bgu.ac.il

Footnotes

*   Supported by the EPSRC grant no. EP C52800X 1