Hostname: page-component-76fb5796d-5g6vh Total loading time: 0 Render date: 2024-04-25T08:01:29.767Z Has data issue: false hasContentIssue false
  • English
  • Français

Some results on permutation group isomorphism and categoricity

Published online by Cambridge University Press:  12 March 2014

Anand Pillay  and
Mark D. Schlatter
Anand Pillay
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street (MC-382), Urbana, Illinois 61801-2975, USA, E-mail: pillay@rriath.uiuc.edu
Mark D. Schlatter
Affiliation:
Department of Mathematics, Centenary College of Louisiana, 2911 Centenary Blvd. Shreveport, Louisiana 71134, USA, E-mail: mschlat@centenary.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We extend Morley's Theorem to show that if a theory is κ-p-categorical for some uncountable cardinal κ, it is uncountably categorical. We then discuss ω-p-categoricity and provide examples to show that similar extensions for the Baldwin-Lachlan and Lachlan Theorems are not possible.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 67 , Issue 3 , September 2002 , pp. 910 - 914
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

[C-K]Chang, C. and Keisler, H., Model theory, North-Holland, 1973.Google Scholar
[P]Pillay, A., An introduction to stability theory, Clarendon Press, 1983.Google Scholar
[S]Schlatter, M., A many permutation group result for unstable theories, this Journal, vol. 63 (1998), pp. 694–708.Google Scholar