Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-11T02:55:29.898Z Has data issue: false hasContentIssue false
  • English
  • Français

Classification theory and 0#

Published online by Cambridge University Press:  12 March 2014

Sy D. Friedman ,
Tapani Hyttinen  and
Mika Rautila
Sy D. Friedman
Affiliation:
Institute for Logic, University of Vienna, Waehringer Strasse 25, A-1090 Vienna, Austria, E-mail: sdf@logic.univie.ac.at, URL http://www.logic.univie.ac.at/~sdf/
Tapani Hyttinen
Affiliation:
Department of Mathematics, University of Helsinki, P.O.Box 4, 00014 HelsinkiFinland, E-mail: tapani.hyttinen@helsinki.fi
Mika Rautila
Affiliation:
Department of Mathematics, University of Helsinki, P.O.Box 4, 00014 HelsinkiFinland Stonesoft Corporation, Itälahdenkatu 22 A, 00210 HelsinkiFinland
Get access Rights & Permissions [Opens in a new window]

Abstract

We characterize the classifiability of a countable first-order theory T in terms of the solvability (in the sense of [2]) of the potential-isomorphism problem for models of T.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 68 , Issue 2 , June 2003 , pp. 580 - 588
Copyright
Copyright © Association for Symbolic Logic 2003

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

[1]Baldwin, J. T., Laskowski, M. C.. and Shelah, S., Forcing isomorphism, this Journal, vol. 58 (1993). no. 4, pp. 1291–1301.Google Scholar
[2]Friedman, Sy D., Cardinal-preserving extensions. Preprint.Google Scholar
[3]Huuskonen, T., Hyttinen, T., and Rautila, M., On potential isomorphism and non-structure. Archive for Mathematical Logic, to appear.Google Scholar
[4]Hyttinen, T. and Tuuri, H., Constructing strongly equivalent nonisomorphic models for unstable theories, Annal of Pure and Applied Logic, vol. 52 (1991), no. 3, pp. 203–248.CrossRefGoogle Scholar
[5]Laskowski, M. C. and Shelah, S., Forcing isomorphism. II, this Journal, vol. 61 (1996), no. 4, pp. 1305–1320.Google Scholar
[6]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
[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.CrossRefGoogle Scholar
[8]Shelah, S., Existence of many L ∞, λ-equivalent, nonisomorphic models of T of power λ. Annals of Pure and Applied Logic, vol. 34 (1987), no. 3, pp. 291–310.CrossRefGoogle Scholar
[9]Shelah, S., Tuuri, H., and Väänänen, J., On the number of automorphisms of uncountable models, this Journal, vol. 58 (1993), no. 4, pp. 1402–1418.Google Scholar