Hostname: page-component-7b7567c8c-kwt9d Total loading time: 0 Render date: 2026-11-14T12:11:08.994Z Has data issue: false hasContentIssue false
  • English
  • Français

On minimal structures

Published online by Cambridge University Press:  12 March 2014

Oleg V. Belegradek
Oleg V. Belegradek*
Affiliation:
Department of Mathematics, Kemerovo State University, Kemerovo, Russia 650043, E-mail: beleg@kaskad.uucp.stanet.ru
Get accessRights & Permissions [Opens in a new window]

Abstract

For any countable transitive complete theory T with infinite models and the finite model property, we construct a minimal structure M such that the theory of M is small if and only if T is small, and is λ-stable if and only if T is λ-stable. This gives a series of new examples of minimal structures.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 63 , Issue 2 , June 1998, pp. 421 - 426
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.)

Article purchase

Temporarily unavailable

References

REFERENCES

[1] Baldwin, J. T. and Lachlan, A. H., On strongly minimal sets, this Journal, vol. 36 (1971), pp. 79–96.Google Scholar
[2] Marsh, W. E., On ω1-categorical and not ω-categorical theories, Ph.D. thesis , Dartmouth College, 1966.Google Scholar
[3] Prest, M., Model theory and modules, London Mathematical Society Lecture Notes Series, no. 130, Cambridge University Press, Cambridge, 1988.Google Scholar
[4] Zil'ber, B. I. and Smurov, V. P., On minimal structures, Ninth all-union conference on mathematical logic, Nauka, Leningrad, 1988, in Russian, p. 65.Google Scholar