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A many permutation group result for unstable theories

Published online by Cambridge University Press:  12 March 2014

Mark D. Schlatter
Mark D. Schlatter*
Affiliation:
Department of Mathematics, University of California at Berkeley, Berkeley, CA 94720, USA Division of Mathematics and Computer Science, Truman State University, Kirksville, MO 63501, USA, E-mail: [email protected]
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Abstract

We extend Shelah's first many model result to show that an unstable theory has 2κ many non-permutation group isomorphic models of size κ, where κ is an uncountable regular cardinal.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 63 , Issue 2 , June 1998 , pp. 694 - 708
Copyright
Copyright © Association for Symbolic Logic 1998

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References

REFERENCES

[1] Cherlin, G. and Lachlan, A. H., Stable finitely homogeneous structures, Transactions of the American Mathematical Society, vol. 296 (1986), pp. 815–850.Google Scholar
[2] Hodges, W., Model theory, Cambridge University Press, 1993.Google Scholar
[3] Jech, T., Set theory, Academic Press, Inc., 1978.Google Scholar
[4] Kaye, R. and Macpherson, D. (editors), Automorphisms of first-order structures, Oxford University Press, 1994.Google Scholar
[5] Knight, J. and Lachlan, A. H., Shrinking, stretching, and codes for homogeneous structures, Classification theory: Proceedings of the U.S.-Israel workshop on model theory in mathematical logic held in Chicago, December 15–19, 1985, Lecture Notes in Mathematics, no. 1292, Springer-Verlag, Berlin, 1985, pp. 192–229.Google Scholar
[6] Shelah, S., Stability, the f.c.p., and superstability: model theoretic properties of formulas in first order theory, Annals of Mathematical Logic, vol. 3 (1970), pp. 271–362.10.1016/0003-4843(71)90015-5Google Scholar
[7] Shelah, S., The number of non-isomorphic models of an unstable first-order theory, Israel Journal of Mathematics, vol. 9 (1971), pp. 473–487.Google Scholar