Hostname: page-component-54dcc4c588-nx7b4 Total loading time: 0 Render date: 2025-09-26T07:25:30.521Z Has data issue: false hasContentIssue false
  • English
  • Français

Vaught's conjecture for modules over a serial ring

Published online by Cambridge University Press:  12 March 2014

Vera Puninskaya
Vera Puninskaya*
Affiliation:
Chair of Algebra, Moscow State University, 119899, Moscow, Russia, E-mail: punins@orc.ru
Get access Rights & Permissions [Opens in a new window]

Abstract

It is proved that Vaught's conjecture is true for modules over an arbitrary countable serial ring. It follows from the structural result that every module with few models over a (countable) serial ring is ω-stable.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 1 , March 2000 , pp. 155 - 163
Copyright
Copyright © Association for Symbolic Logic 2000

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 McKenzie, R.N., Counting models in universal Horn classes, Algebra Universalis, vol. 15 (1982), pp. 359–384.CrossRefGoogle Scholar
[2]Buechler, S., The classification of small weakly minimal sets III. Modules, this Journal, vol. 53 (1988), no. 3, pp. 975–979.Google Scholar
[3]Eklof, P. and Herzog, I., Model theory of modules over a serial ring, Annals of Pure and Applied Logic, vol. 72 (1995), pp. 145–176.CrossRefGoogle Scholar
[4]Facchini, A. and Puninski, G., Σ-pure-injective modules over serial rings, Abelian groups and modules (Facchini, A. and Menini, C., editors), Kluwer Academic Publishers, Dordrecht, 1995, pp. 145–162.CrossRefGoogle Scholar
[5]Faith, C., Algebra: Rings, modules and categories II, Springer, 1976.Google Scholar
[6]Garavaglia, S., Decomposition of totally transcendental modules, this Journal, vol. 45 (1980), no. 1, pp. 155–164.Google Scholar
[7]Harrington, L., Makkai, M., and Shelah, S., A proof of Vaught's conjecture for ω-stable theories, Israel Journal of Mathematics, vol. 49 (1984), pp. 259–280.Google Scholar
[8]Herzog, I., Modules with few types, Journal of Algebra, vol. 149 (1992), pp. 358–370.CrossRefGoogle Scholar
[9]Prest, M., Model theory and modules, Cambridge University Press, 1988.CrossRefGoogle Scholar
[10]Rothmaler, Ph., Some model theory of modules. II. On stability and categoricity of flat modules, this Journal, vol. 48 (1983), no. 4, pp. 970–985.Google Scholar
[11]Rothmaler, Ph., Independence in U-rk 1 modules with few types, Technical report, Christian–Albrechts–Universität, Kiel, 1987, preprint.Google Scholar
[12]Rothmaler, Ph., A trivial remark on purity, Proceedings of Ninth Easter Conference on Model Theory, Seminarber, vol. 112, Berlin, 1991.Google Scholar
[13]Rowen, L.H., Ring theory, Academic Press, 1991.Google Scholar
[14]Warfield, R.B., Serial rings and finitely presented modules, Journal of Algebra, vol. 37 (1975), no. 3, pp. 187–222.CrossRefGoogle Scholar
[15]Ziegler, M., Model theory of modules, Annals of Pure and Applied Logic, vol. 26 (1984), pp. 149–213.CrossRefGoogle Scholar