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On almost orthogonality in simple theories

Published online by Cambridge University Press:  12 March 2014

Itay Ben-Yaacov
Affiliation:
Massachusetts Institute of Technology, Department of Mathematics, 77 Massachusetts Avenue, Room 2-101, Cambridge, Mass, 02139-4307, USA, E-mail: pezz@math.mit.edu, URL: http://www-math.mit.edu/~pezz
Frank O. Wagner
Affiliation:
Institut Girard Desargues, Université Lyon, 1, 21 Avenue Claude Bernard, 69622 Villeurbanne Cedex, France, E-mail: wagner@desargues.univ-lyon1.fr
Corresponding

Abstract.

1. We show that if p is a real type which is internal in a set Σ of partial types in a simple theory, then there is a type p′ interbounded with p, which is finitely generated over Σ, and possesses a fundamental system of solutions relative to Σ.

2. If p is a possibly hyperimaginary Lascar strong type, almost Σ-internal, but almost orthogonal to Σω, then there is a canonical non-trivial almost hyperdefinable polygroup which multi-acts on p while fixing Σ generically In case p is Σ-internal and T is stable, this is the binding group of p over Σ.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2004

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References

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