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The Group Configuration in Simple Theories and its Applications

Published online by Cambridge University Press:  15 January 2014

Itay Ben-Yaacov ,
Ivan Tomašić  and
Frank O. Wagner
Itay Ben-Yaacov
Affiliation:
Équipe de Logique Mathematique, UFR de Mathématiques (Case 7012), Université Paris 7, 2 Place Jussieu, 75251 Paris Cedex 05, FranceE-mail: pezz@logique.jussieu.fr
Ivan Tomašić
Affiliation:
School of Mathematics, University of Leeds, Leeds LS2 9JT, United KingdomE-mail: itomasic@amsta.leeds.ac.uk
Frank O. Wagner
Affiliation:
Institut Girard Desargues, Université Claude Bernard(Lyon 1), Bât. Jean Braconnier, 21 Av. Claude Bernard, 69622 Villeurbanne Cedex FranceE-mail: wagner@desargues.univ-lyon1.fr
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Abstract

In recent work, the authors have established the group configuration theorem for simple theories, as well as some of its main applications from geometric stability theory, such as the binding group theorem, or, in the ω-categorical case, the characterization of the forking geometry of a finitely based non-trivial locally modular regular type as projective geometry over a finite field and the equivalence of pseudolinearity and local modularity.

The proof necessitated an extension of the model-theoretic framework to include almost hyperimaginaries, and the study of polygroups.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 8 , Issue 2 , June 2002 , pp. 283 - 298
Copyright
Copyright © Association for Symbolic Logic 2002

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References

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