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On almost orthogonality in simple theories

Published online by Cambridge University Press:  12 March 2014

Itay Ben-Yaacov  and
Frank O. Wagner
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
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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.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 69 , Issue 2 , June 2004 , pp. 398 - 408
Copyright
Copyright © Association for Symbolic Logic 2004

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References

REFERENCES

[1]Ben-Yaacov, Itay, Group configurations and germs in simple theories, this Journal, vol. 67 (2002), no. 4, pp. 1581–1600.Google Scholar
[2]Ben-Yaacov, Itay, On the fine structure of the polygroup blow-up, Archive for Mathematical Logic, vol. 42 (2003), pp. 649–663.CrossRefGoogle Scholar
[3]Ben-Yaacov, Itay, Tomašić, Ivan, and Wager, Frank O., Constructing an almost hyperdefinable group, preprint.Google Scholar
[4]Bergman, George M. and Lenstra, Hendrik W. Jr., Subgroups close to normal subgroups, Journal of Algebra, vol. 127 (1989), pp. 80–97.CrossRefGoogle Scholar
[5]Buechler, Steven, Essential stability theory, Springer-Verlag, Berlin, 1996.CrossRefGoogle Scholar
[6]Buechler, Steven, Pillay, Anand, and Wagner, Frank O., Supersimple theories, Journal of the American Mathematical Society, vol. 14 (2001), pp. 109–124.CrossRefGoogle Scholar
[7]Hart, Bradd, Kim, Byunghan, and Pillay, Anand, Coordinatisation and canonical bases in simple theories, this Journal, vol. 65 (2000), pp. 293–309.Google Scholar
[8]Pillay, Anand, Geometric stability theory, Clarendon Press, 1996.CrossRefGoogle Scholar
[9]Poizat, Bruno, Groupes stables, Nur al-Mantiq wal-Ma'rifah, 1987.Google Scholar
[10]Schlichting, G., Operationen mit periodischen Stabilisatoren, Archiv der Mathematik, vol. 34 (1980), pp. 97–99.CrossRefGoogle Scholar
[11]Shami, Ziv and Wager, Frank O., On the binding group in simple theories, this Journal, vol. 67 (2002), no. 3, pp. 1016–1024.Google Scholar
[12]Tomašić, Ivan and Wagner, Frank O., Applications of the group configuration theorem in simple theories, Journal of Mathematical Logic, to appear.Google Scholar
[13]Wager, Frank O., Simple theories, Kluwer Academic Publishers, 2000.CrossRefGoogle Scholar