Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-13T07:03:57.475Z Has data issue: false hasContentIssue false
  • English
  • Français

Kueker's conjecture for stable theories

Published online by Cambridge University Press:  12 March 2014

Ehud Hrushovski
Ehud Hrushovski*
Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
*
Department of Mathematics, Princeton University, Princeton, New Jersey 08544
Get access Rights & Permissions [Opens in a new window]

Abstract

Kueker's conjecture is proved for stable theories, for theories that interpret a linear ordering, and for theories with Skolem functions. The proof of the stable case involves certain results on coordinatization that are of independent interest.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 54 , Issue 1 , March 1989 , pp. 207 - 220
Copyright
Copyright © Association for Symbolic Logic 1989

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

[BL] Baldwin, J. and Lachlan, A., On strongly minimal sets, this Journal, vol. 36 (1971), pp. 79–96.Google Scholar
[Bu] Buechler, S., Kueker's conjecture for superstable theories, this Journal, vol. 49 (1984), pp. 930–934.Google Scholar
[H] Hrushovski, E., Contributions to stable model theory, Ph.D. thesis, University of California, Berkeley, California, 1986.Google Scholar
[K] Keisler, H. J., Logic with the quantifier “there exist uncountably many”, Annals of Mathematical Logic, vol. 1 (1970), pp. 1–94.CrossRefGoogle Scholar
[Kn] Knight, J., proof of Kueker's conjecture for linear orderings, announced in [Bu].Google Scholar
[Ku] Kueker, D., On small extensions, this Journal (to appear).Google Scholar
[Ls] Lascar, D., Rank and definability in superstable theories, Israel Journal of Mathematics, vol. 23 (1976), pp. 53–87.CrossRefGoogle Scholar
[M] Makkai, M., A survey of basic stability theory, with particular emphasis on orthogonality and regular types, Israel Journal of Mathematics, vol. 49 (1984), pp. 181–238.CrossRefGoogle Scholar
[Mo] Morley, M., Categoricity in power, Transactions of the American Mathematical Society, vol. 114 (1965), pp. 514–538.CrossRefGoogle Scholar
[Ry] Ryll-Nardzewski, C., On categoricity in power ≤ ℵ0, Bulletin de l'Académie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques et Physiques, vol. 7 (1959), pp. 545–548.Google Scholar
[Sh] Shelah, S., Classification theory and the number of non-isomorphic models, North-Holland, Amsterdam, 1978.Google Scholar
[V] Vaught, R. L., Denumerable models of complete theories, Infinitistic methods (proceedings, Warsaw, 1959), PWN, Warsaw, and Pergamon Press, Oxford, 1961, pp. 303–321.Google Scholar