Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-16T17:03:16.030Z Has data issue: false hasContentIssue false
  • English
  • Français

Automorphism properties of stationary logic

Published online by Cambridge University Press:  12 March 2014

Martin Otto
Martin Otto*
Affiliation:
Institut für Mathematische Logik, Universität Freiburg, W-7800 Freiburg, Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

By means of an Ehrenfeucht-Mostowski construction we obtain an automorphism theorem for a syntactically characterized class of Laa-theories comprising in particular the finitely determinate ones. Examples of Laa-theories with only rigid models show this result to be optimal with respect to a classification in terms of prenex quantifier type: Rigidity is seen to hinge on quantification of type … ∀ … stat … permitting of the parametrization of families of disjoint stationary systems by the elements of the universe.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 57 , Issue 1 , March 1992 , pp. 231 - 237
Copyright
Copyright © Association for Symbolic Logic 1992

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

[BKM]Barwise, K. J., Kaufmann, M. J., and Makkai, M., Stationary logic, Annals of Mathematical Logic, vol. 13 (1978), pp. 171–224.CrossRefGoogle Scholar
[BT]Baumgartner, J. E. and Taylor, A. D., Saturation properties of ideals in generic extensions. I, Transactions of the American Mathematical Society, vol. 270 (1982), pp. 557–574.CrossRefGoogle Scholar
[Eb]Ebbinghaus, H.-D., On models with large automorphism groups, Archiv für Mathematische Logik und Grundlagenforschung, vol. 14 (1971), pp. 179–197.CrossRefGoogle Scholar
[EhM]Ehrenfeucht, A. and Mostowski, A., Models of axiomatic theories admitting automorphisms, Fundamenta Mathematicae, vol. 43 (1956), pp. 50–68.CrossRefGoogle Scholar
[EkM]Eklof, P. C. and Mekler, A. H., Stationary logic of finitely determinate structures, Annals of Mathematical Logic, vol. 17 (1979), pp. 227–269.CrossRefGoogle Scholar
[F]Flum, J., Die Automorphismenmenge der Modelle einer LQ-Theorie, Archiv für Mathematische Logik und Grundlagenforschung, vol. 15 (1972), pp. 83–85.CrossRefGoogle Scholar
[H]Hodges, W., Models built on linear orderings, Ordered sets and their applications (Pouzet, M. and Richard, D., editors), North-Holland, Amsterdam, 1984, pp. 207–234.Google Scholar
[K]Kaufmann, M.J., The quantifier “there exist uncountably many” and some of its relatives, Model-theoretic logics (Barwise, J. and Feferman, S., editors), Springer-Verlag, Berlin, 1985, pp. 123–176.Google Scholar
[S71]Shelah, S., Two-cardinal and power-like models: compactness and large groups of automorphisms, Notices of the American Mathematical Society, vol. 18 (1971), p. 425. (Abstract #71T-E15)Google Scholar
[S75]Shelah, S., Generalized quantifiers and compact logic, Transactions of the American Mathematical Society, vol. 204 (1975), pp. 342–364.CrossRefGoogle Scholar
[SK]Shelah, S. and Kaufmann, M. J., The Hanf number of stationary logic, Notre Dame Journal of Formal Logic, vol. 27 (1986), pp. 111–123.Google Scholar