Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-14T13:25:12.473Z Has data issue: false hasContentIssue false
  • English
  • Français

Flat Morley sequences

Published online by Cambridge University Press:  12 March 2014

Ludomir Newelski
Ludomir Newelski*
Affiliation:
Mathematical Institute of Wroclaw University, Pl.Grunwaldzki 2/4, 50–384, Wrocław, Poland E-mail: [email protected] Mathematical Institute of the Polish Academy of Sciences, Ul. Kopernika 18, WrocŁaw, Poland
Get access Rights & Permissions [Opens in a new window]

Abstract

Assume T is a small superstable theory. We introduce the notion of a flat Morley sequence, which is a counterpart of the notion of an infinite Morley sequence in a type p, in case when p is a complete type over a finite set of parameters. We show that for any flat Morley sequence Q there is a model M of T which is τ-atomic over {Q}. When additionally T has few countable models and is 1-based, we prove that within M there is an infinite Morley sequence I, with I ⊂ dcl(Q), such that M is prime over I.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 3 , September 1999 , pp. 1261 - 1279
Copyright
Copyright © Association for Symbolic Logic 1999

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

[Bu] Buechler, S., Vaught's conjecture for superstable theories offinite rank, preprint, 1993.Google Scholar
[H-P] Hrushovski, E. and Pillay, A., Weakly normal groups, Logic Colloquium 1985, North Holland, Amsterdam, The Paris Logic Group ed., 1987, pp. 233–244.Google Scholar
[L-P] Lascar, D. and Poizat, B., An introduction to forking, this Journal, vol. 44 (1979), pp. 330–350.Google Scholar
[Nel] Newelski, L., A proof of Saffe'S conjecture, Fundamenta Mathematicae, vol. 134 (1990), pp. 143–155.CrossRefGoogle Scholar
[Ne2] Newelski, L., A model and its subset, this Journal, vol. 57 (1992), pp. 644–658.Google Scholar
[Ne3] Newelski, L., Scott analysis of pseudo-types, this Journal, vol. 58 (1993).Google Scholar
[Ne4] Newelski, L., Meager forking, Annals of Pure and Applied Logic, vol. 70 (1994), pp. 141–175.CrossRefGoogle Scholar
[Ne5] Newelski, L., -rank and meager types, Fundamenta Mathematicae, vol. 146 (1995), pp. 121–139.CrossRefGoogle Scholar
[Ne7] Newelski, L., -rank andmeager groups, Fundamenta Mathematicae, vol. 150 (1996), pp. 149–171.CrossRefGoogle Scholar
[Ne6] Newelski, L., On atomic or saturated sets, this Journal, vol. 61 (1996), pp. 318–333.Google Scholar
[Ne8] Newelski, L., -gap conjecture and m-normal theories, Israel Journal of Mathematics, accepted.Google Scholar
[Ne9] Newelski, L., Vaught's conjecture for some meager groups, Israel Journal of Mathematics, accepted.Google Scholar
[Sh] Shelah, S., Classification theory, 2nd ed., North Holland, 1990.Google Scholar
[SHM] Shelah, S., Harrington, L., and Makkai, M., A proof of Vaught's conjecture for ℵ0-stable theories, Israel Journal of Mathematics, vol. 49 (1984), pp. 259–278.CrossRefGoogle Scholar