Hostname: page-component-68945f75b7-l9cl4 Total loading time: 0 Render date: 2024-08-05T18:32:20.993Z Has data issue: false hasContentIssue false
  • English
  • Français

Definability and definable groups in simple theories

Published online by Cambridge University Press:  12 March 2014

Anand Pillay
Anand Pillay*
Affiliation:
University of Illinois at Urbana-Champaign, Department of Mathematics, Altgeld Hall, 1409 West Green Street, Urbana, IL 61801, USA E-mail: pillay@math.uiuc.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We continue the study of simple theories begun in [3] and [5]. We first find the right analogue of definability of types. We then develop the theory of generic types and stabilizers for groups definable in simple theories. The general ideology is that the role of formulas (or definability) in stable theories is replaced by partial types (or ∞-definability) in simple theories.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 63 , Issue 3 , September 1998 , pp. 788 - 796
Copyright
Copyright © Association for Symbolic Logic 1998

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]Hrushovski, E., manuscript on PAC structures, 1992.Google Scholar
[2]Hrushovski, E. and Pillay, A., Groups definable in local fields and finite fields, Israel Journal of Mathematics, vol. 85 (1994), pp. 203–262.CrossRefGoogle Scholar
[3]Kim, B., Forking in simple unstable theories, Journal of the London Mathematical Society, to appear.Google Scholar
[4]Kim, B., Simple first order theories, Ph.D. thesis, University of Notre Dame, 1996.Google Scholar
[5]Kim, B. and Pillay, A., Simple theories, Annals of Pure and Applied Logic, vol. 88 (1977), pp. 149–164.CrossRefGoogle Scholar
[6]Shelah, S., Simple unstable theories, Annals of Mathematical Logic, vol. 19 (1980), pp. 177–203.CrossRefGoogle Scholar