Hostname: page-component-8448b6f56d-tj2md Total loading time: 0 Render date: 2024-04-24T20:50:05.967Z Has data issue: false hasContentIssue false

Local superssimplicity and related concepts

Published online by Cambridge University Press:  12 March 2014

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

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.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2002

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Buechler, Steven, Lascar strong types in some simple theories, this Journal, vol. 64 (1999), pp. 817824.Google Scholar
[2]Casanovas, Enrique, The number of types in simple theories, Annals of Pure and Applied Logic, vol. 98 (1999), pp. 6986.CrossRefGoogle Scholar
[3]Casanovas, Enrique and Kim, Byunghan, A supersimple nonlow theory, Notre Dame Journal of Formal Logic, vol. 39 (1998), pp. 507518.CrossRefGoogle Scholar
[4]Evans, David and Wagner, Frank O., Supersimple ω-categorical groups and theories, this Journal, vol. 65 (2000), no. 2, pp. 767776.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. 297303.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. 483500.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