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Local superssimplicity and related concepts

Published online by Cambridge University Press:  12 March 2014

Enrique Casanovas  and
Frank O. Wagner
Enrique Casanovas
Affiliation:
Departament de Lògica, Història i Filosofia de la Ciència, Universitat de Barcelona, Baldiri Reixac S/N. 08028 Barcelona, Spain, E-mail: casanova@mat.ub.es
Frank O. Wagner
Affiliation:
Institut Girard Desargues, Université Claude Bernard (Lyon1), 21, Avenue Claude Bernard, 69622 Villeurbanne-Cedex, France, E-mail: wagner@desargues.univ-lyon1.fr, URL: http://www.desargues.univ-lyonl.fr/home/wagner/fowaf.html
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Abstract

We study local strengthenings of the simplicity condition. In particular, we define and study a local Lascar rank, as well as short, low. supershort and superlow theories. An example of a low non supershort theory is given.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 67 , Issue 2 , June 2002 , pp. 744 - 758
Copyright
Copyright © Association for Symbolic Logic 2002

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References

REFERENCES

[1]Buechler, Steven, Lascar strong types in some simple theories, this Journal, vol. 64 (1999), pp. 817–824.Google Scholar
[2]Casanovas, Enrique, The number of types in simple theories, Annals of Pure and Applied Logic, vol. 98 (1999), pp. 69–86.CrossRefGoogle Scholar
[3]Casanovas, Enrique and Kim, Byunghan, A supersimple nonlow theory, Notre Dame Journal of Formal Logic, vol. 39 (1998), pp. 507–518.CrossRefGoogle Scholar
[4]Evans, David and Wagner, Frank O., Supersimple ω-categorical groups and theories, this Journal, vol. 65 (2000), no. 2, pp. 767–776.Google Scholar
[5]Herwig, Bernhard, Loveys, James G., Pillay, Anand, Tanovic, Predrag, and Wagner, Frank O., Stable theories without dense forking chains, Arch. Math. Logic, vol. 31 (1992), pp. 297–303.CrossRefGoogle Scholar
[6]Kim, Byunghan, Simple first order theories, Ph.D. thesis, University of Notre Dame, USA, 1996.Google Scholar
[7]Macpherson, H. Dugald, Absolutely ubiquitous structures and ℵ0-categorical groups, Quart. J. Math. Oxford (2), vol. 39 (1988), pp. 483–500.CrossRefGoogle Scholar
[8]Wagner, Frank O., Stable groups, London Mathematical Society Lecture Notes 240, Cambridge University Press, Cambridge, United Kingdom, 1997.Google Scholar
[9]Wagner, Frank O., Simple theories, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000.CrossRefGoogle Scholar