Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-16T13:09:25.879Z Has data issue: false hasContentIssue false
  • English
  • Français

Regular types in nonmultidimensional ω-stable theories

Published online by Cambridge University Press:  12 March 2014

Anand Pillay
Anand Pillay*
Affiliation:
University of Notre Dame, Notre Dame, Indiana 46556
Get access Rights & Permissions [Opens in a new window]

Abstract

We define a hierarchy on the regular types of an ω-stable nonmultidimensional theory, using generalised notions of algebraic and strongly minimal formulae. As an application we show that any resplendent model of an ω-stable finite-dimensional theory is saturated.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 49 , Issue 3 , September 1984 , pp. 880 - 891
Copyright
Copyright © Association for Symbolic Logic 1984

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. and Lachlan, A. H.. Strongly minimal sets, this Journal, vol. 36 (1971), pp. 79–96.Google Scholar
[2]Bouscaren, E., Modules existentiellement clos: types et modèles premiers, Thèse du 3ième cycle, Université Paris VII, Paris, 1979.Google Scholar
[3]Buechler, S., The structure and construction of models, Ph.D. thesis, University of Maryland, College Park, Maryland, 1981.Google Scholar
[3]Buechler, S., Resplendency and recursive definability in ω-stable theories, preprint, 1982.Google Scholar
[4]Knight, J. F., Theories whose resplendent models are homogeneous, Israel Journal of Mathematics, vol. 42 (1982), pp. 151–161.CrossRefGoogle Scholar
[5]Knight, J. F. and Lachlan, A. H., Recursive definability in ω-stable theories of finite rank, preprint, 1982.Google Scholar
[6]Lachlan, A. H., Spectra of ω-stable theories, Zeitschrift für Mathematische Logik. und Grundlagen der Mathematik, vol. 24 (1978), pp. 129–139.CrossRefGoogle Scholar
[7]Lascar, D., Ordre de Rudin-Keisler et poids dans les théories stables, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 28 (1982), pp. 413–430.CrossRefGoogle Scholar
[8]Lascar, D., Le rang U et poids (to appear).Google Scholar
[9]Lascar, D. and Poizat, B., An introduction to forking, this Journal, vol. 44 (1979), pp. 330–350.Google Scholar
[10]Makkai, M., A survey of basic stability theory (to appear).Google Scholar
[11]Pillay, A., An introduction to stability theory, Oxford University Press, Oxford, 1983.Google Scholar
[12]Pillay, A., The models of an ω-stable nonmultidimensional theory, Groupe d'étude: théories stables. III (Poizat, B., editor), Secrétariat Mathématique, Paris (to appear).Google Scholar
[13]Pillay, A. and Prest, M., Forking and pushouts in modules, Proceedings of the London Mathematical Society, ser. 3, vol. 46 (1983), 365–384.CrossRefGoogle Scholar
[14]Prest, M., The generalised RK-order, orthogonality and regular types for modules (to appear).Google Scholar
[15]Shelah, S., Classification theory and the number of nomsomorphic models, North-Holland, Amsterdam, 1978.Google Scholar
[16]Shelah, S., The spectrum problem. II: The infinite depth case (to appear).Google Scholar
[17]Ziegler, M., The model theory of modules (to appear).Google Scholar
[18]Bouscaren, E. and Lascar, D., Countable models of an ω-stable nonmultidimensional theory, this Journal, vol. 48 (1983), pp. 197–205.Google Scholar
[19]Poizat, B., Paires de structures stables, this Journal, vol. 48 (1983), pp. 239–249.Google Scholar