Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-28T03:04:08.940Z Has data issue: false hasContentIssue false
  • English
  • Français

INTERPRETABLE GROUPS, STABLY EMBEDDED SETS, AND VAUGHTIAN PAIRS

Published online by Cambridge University Press:  08 August 2003

BERNHARD HERWIG ,
EHUD HRUSHOVSKI  and
DUGALD MACPHERSON
BERNHARD HERWIG
Affiliation:
Am Gonsenheimer Spiess 18, 55122 MainzGermany e-mail: [email protected]
EHUD HRUSHOVSKI
Affiliation:
Department of Mathematics, Hebrew University, Jerusalem, Israel e-mail: [email protected]
DUGALD MACPHERSON
Affiliation:
Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT e-mail: [email protected]
Get access

Abstract

The paper concerns sufficiently saturated structures M over a countable language with a unary predicate P. It is shown that if $P(M)$ is stably embedded and there are no Vaughtian pairs with respect to P, then an infinite group is interpretable over M (in an infinitary sense of ‘interpretable’). Also, it is shown that if M is $\omega$-categorical, $f\,{:}\,D\,{\longrightarrow}\,P$ is a 0-definable map with finite fibres, and $P(M)$ is stably embedded but D is not, then some infinite group is first-order interpretable over M.

Keywords

03C52
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 68 , Issue 1 , August 2003 , pp. 1 - 11
Copyright
The London Mathematical Society 2003

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.)

Footnotes

The research of the first and third authors was partially supported by EPSRC grant GR/K60503. This research was conducted by Ehud Hrushovski as a CMI Prize Fellow, for the Clay Mathematics Institute.