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A note on Lascar strong types in simple theories

Published online by Cambridge University Press:  12 March 2014

Byunghan Kim
Byunghan Kim*
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720-3840, USA E-mail: bkim@math.berkeley.edu
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Abstract

Let T be a countable, small simple theory. In this paper, we prove that for such T, the notion of Lascar strong type coincides with the notion of strong type, over an arbitrary set.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 63 , Issue 3 , September 1998 , pp. 926 - 936
Copyright
Copyright © Association for Symbolic Logic 1998

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References

REFERENCES

[1]Cherlin, G. and Hrushovski, E., Lie coordinatised structures, in preparation.Google Scholar
[2]Kantor, W. M., Liebeck, M. W., and Macpherson, H. D., “ℵ0-categorical structures smoothly approximated by finite structures, Proceedings of the London Mathematical Society, vol. 3 (1989), no. 59, pp. 439–463.CrossRefGoogle Scholar
[3]Kim, B., Forking in simple unstable theories, to appear in Journal of the London Mathematical Society.Google Scholar
[4]Kim, B., Recent results on simple first order theories, Model theory of groups and automorphism groups, London Mathematical Society Lecture Note Series, no. 244, Cambridge University Press, 1997, pp. 202–212.CrossRefGoogle Scholar
[5]Kim, B. and Pillay, A., Simple theories, to appear in Annals of Pure and Applied Logic.Google Scholar
[6]Lascar, D., On the category of models of a complete theory, this Journal, vol. 47 (1982), pp. 249–266.Google Scholar
[7]Lascar, D., The group of automorphisms of a relational saturated structure, Finite and infinite combinatorics in sets and logic, NATO ASI Series C: Mathematical and Physical Sciences, no. 411, Kluwer Academic Publishers, Dordrecht, 1993, pp. 225–236.CrossRefGoogle Scholar
[8]Lascar, D., Recovering the action of an automorphism group, Logic: from foundations to applications, Oxford University Press, New York, 1996, pp. 313–326.CrossRefGoogle Scholar
[9]Pillay, A. and Poizat, B., Pas d'imaginaires dans l'infinil, this Journal, vol. 52 (1987), pp. 400–403.Google Scholar
[10]Shelah, S., Simple unstable theories, Annals of Mathematical Logic, vol. 19 (1980), pp. 177–203.CrossRefGoogle Scholar
[11]Shelah, S., Classification theory, revised ed., North-Holland, Amsterdam, 1990.Google Scholar