Hostname: page-component-848d4c4894-75dct Total loading time: 0 Render date: 2024-06-04T12:19:08.954Z Has data issue: false hasContentIssue false
  • English
  • Français

Countable models of trivial theories which admit finite coding

Published online by Cambridge University Press:  12 March 2014

James Loveys  and
Predrag Tanović
James Loveys
Affiliation:
Department of Mathematics and Statistics, Mcgill University, 805 Sherbrooke West, Montreal, Quebec, CanadaH3A 2K6, E-mail: loveys@triples.math.mcgill.ca
Predrag Tanović
Affiliation:
Matematiǩi institut, Knez Mihajlova 35, 11001 Beograd, Yugoslavia, and Department of Mathematics and Statistics, Mcgill University, 805 Sherbrooke West Montreal, Quebec, CanadaH3A 2K6
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove:

Theorem. A complete first order theory in a countable language which is strictly stable, trivial and which admits finite coding hasnonisomorphic countable models.

Combined with the corresponding result or superstable theories from [4] our result confirms the Vaught conjecture for trivial theories which admit finite coding.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 61 , Issue 4 , December 1996 , pp. 1279 - 1286
Copyright
Copyright © Association for Symbolic Logic 1996

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]Baldwin, J. T., Fundamentals of stability theory, Springer-Verlag, 1988.CrossRefGoogle Scholar
[2]Herwig, B., Loveys, J., Pillay, A., Tanovic, P., and Wagner, F., Stable theories without dense forking chains, Archive for Mathematical Logic, vol. 31 (1992).CrossRefGoogle Scholar
[3]Hrushovski, E., Finitely based theories, this Journal, vol. 54 (1989).Google Scholar
[4]Low, L. F. and Pillay, A., Superstable theories with few countable models, Archive for Mathematical Logic, vol. 31 (1992).CrossRefGoogle Scholar
[5]Makkai, M., A survey of basic stability theory with particular emphasis on orthogonality and regular types, Israel Journal of Mathematics, vol. 49 (1984).CrossRefGoogle Scholar
[6]Pillay, A., Countable models of one-based theories, Archive for Mathematical Logic, vol. 31 (1992).CrossRefGoogle Scholar
[7]Shelah, S., Classification theory and the number of nonisomorphic models, North-Holland, 1978.Google Scholar
[8]Shelah, S., Harrington, L., and Makkai, M., A proof of Vaught's conjecture for totally transcendental theories, Israel Journal of Mathematics, vol. 49 (1984).CrossRefGoogle Scholar