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Classification theory and 0#

  • Sy D. Friedman (a1), Tapani Hyttinen (a2) and Mika Rautila (a3) (a4)

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.

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[1]Baldwin, J. T., Laskowski, M. C.. and Shelah, S., Forcing isomorphism, this Journal, vol. 58 (1993). no. 4, pp. 12911301.
[2]Friedman, Sy D., Cardinal-preserving extensions. Preprint.
[3]Huuskonen, T., Hyttinen, T., and Rautila, M., On potential isomorphism and non-structure. Archive for Mathematical Logic, to appear.
[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. 203248.
[5]Laskowski, M. C. and Shelah, S., Forcing isomorphism. II, this Journal, vol. 61 (1996), no. 4, pp. 13051320.
[6]Nadel, M. and Stavi, J., L ∞,λ-equivalence, isomorphism and potential isomorphism. Transactions of the American Mathematical Society, vol. 236 (1978), pp. 5174.
[7]Shelah, S., The number of non-isomorphic models of an unstable first-order theory, Israel journal of Mathematics, vol. 9 (1971), pp. 473487.
[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. 291310.
[9]Shelah, S., Tuuri, H., and Väänänen, J., On the number of automorphisms of uncountable models, this Journal, vol. 58 (1993), no. 4, pp. 14021418.

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