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The strict order property and generic automorphisms

Published online by Cambridge University Press:  12 March 2014

Hirotaka Kikyo
Affiliation:
Department of Mathematical Sciences, Tokai University, 1117 Kitakaname, Hiratsuka, 259-1292, Japan, E-mail: kikyo@ss.u-tokai.ac.jp
Saharon Shelah
Affiliation:
Institute of Mathematics, The Hebrew University, Jerusalem 91904, Israel, E-mail: shelah@sundial.ma.huji.ac.il

Abstract

If T is a model complete theory with the strict order property, then the theory of the models of T with an automorphism has no model companion.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2002

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References

REFERENCES

[1]Chatzidakis, Z., Generic automorphisms of separably closed fields, to appear in the Illinois Journal of Mathematics.Google Scholar
[2]Chatzidakis, Z. and Hrushovski, E., The model theory of difference fields, Transactions of the American Mathematical Society, vol. 351 (1999), pp. 29973071.CrossRefGoogle Scholar
[3]Chatzidakis, Z. and Pillay, A., Generic structures and simple theories, Annals of Pure and Applied Logic, vol. 95 (1998), pp. 7192.CrossRefGoogle Scholar
[4]Kikyo, H., Model companions of theories with an automorphism, this Journal, vol. 65 (2000), pp. 12151222.Google Scholar
[5]Kikyo, H. and Pillay, A., The definable multiplicity property and generic automorphism, Annals of Pure and Applied Logic, vol. 106 (2000), pp. 263273.CrossRefGoogle Scholar
[6]Lascar, D., Autour de la propriété du petit indice, Proceedings of the London Mathematical Society, vol. 62 (1991), pp. 2553.CrossRefGoogle Scholar
[7]Lascar, D., Les beaux automorphismes, Archive for Mathematical Logic, vol. 31 (1991), pp. 5568.CrossRefGoogle Scholar
[8]Macintyre, A., Generic automorphisms of fields, Annals of Pure and Applied Logic, vol. 88 (1997), pp. 165180.CrossRefGoogle Scholar
[9]Shelah, S., Classification theory and the number of non-isomorphic models, North-Holland, Amsterdam, 1978.Google Scholar