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On the number of automorphisms of uncountable models

Published online by Cambridge University Press:  12 March 2014

Saharon Shelah ,
Heikki Tuuri  and
Jouko Väänänen
Saharon Shelah
Affiliation:
Department of Mathematics, Hebrew University of Jerusalem, Jerusalem, Israel
Heikki Tuuri
Affiliation:
Department of Mathematics, University of Helsinki, 00100 Helsinki, Finland
Jouko Väänänen
Affiliation:
Department of Mathematics, University of Helsinki, 00100 Helsinki, Finland
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Abstract

Let σ() denote the number of automorphisms of a model of power ω1. We derive a necessary and sufficient condition in terms of trees for the existence of an with . We study the sufficiency of some conditions for . These conditions are analogous to conditions studied by D. Kueker in connection with countable models.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 58 , Issue 4 , December 1993 , pp. 1402 - 1418
Copyright
Copyright © Association for Symbolic Logic 1993

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References

REFERENCES

[1]Galvin, F., Jech, T. and Magidor, M., An ideal game, this Journal, vol. 43 (1978), pp. 284–292.Google Scholar
[2]Hodges, W. and Shelah, S., Infinite games and reduced products, Annals of Mathematical Logic, vol. 20 (1981), pp. 77–108.CrossRefGoogle Scholar
[3]Hyttinen, T., Games and infinitary languages, Annales Academiae Scientarum Fennicae, Series A I, Mathematica Dissertationes, vol. 64, Academiae Scientarum Fennica, Helsinki, 1987.Google Scholar
[4]Hyttinen, T., Model theory for infinite quantifier languages, Fundamenta Mathematicae, vol. 134 (1990), pp. 125–142.CrossRefGoogle Scholar
[5]Jech, T., Automorphisms of ω 1-trees, Transactions of the American Mathematical Society, vol. 173 (1972), pp. 57–70.Google Scholar
[6]Jech, T., Set theory, Academic Press, New York, 1978.Google Scholar
[7]Karttunen, M., Model theory for infinitely deep languages, Annales Academiae Scientarum Fennicae, Series A I, Mathematica Dissertationes, vol. 50, Academiae Scientarum Fennica, Helsinki, 1984.Google Scholar
[8]Kueker, D., Definability, automorphisms and infinitary languages, The syntax and semantics of infinitary languages (Barwise, J., editor), Springer-Verlag, New York, 1968.Google Scholar
[9]Nadel, M. and Stavi, J., L∞λ-equivalence, isomorphism and potential isomorphism, Transactions of the American Mathematical Society, vol. 236 (1978), pp. 51–74.Google Scholar
[10]Oikkonen, J., How to obtain interpolation for , Logic colloquium '86 (Drake, and Truss, , editors), North-Holland, Amsterdam, 1988.Google Scholar
[11]Väänänen, J., Games and trees in infinitary logic: A survey, Quantifiers (Krynicki, M., Mostowski, M., and Szczerba, L., editors) (to appear).Google Scholar