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A complicated ω-stable depth 2 theory

  • Martin Koerwien (a1)


We present a countable complete first order theory T which is model theoretically very well behaved: it eliminates quantifiers, is ω-stable, it has NDOP and is shallow of depth two. On the other hand, there is no countable bound on the Scott heights of its countable models, which implies that the isomorphism relation for countable models is not Borel.



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[1]Baldwin, J. T., Fundamentals of stability theory, Springer, 1988.
[2]Becker, H. and Kechris, A. S., The descriptive set theory of polish group actions, London Mathematical Society Lecture Notes Series 232, Cambridge University Press, 1996.
[3]Harrington, L. A., Kechris, A. S., and Louveau, A., A Glimm–Effros dichotomy for Borel equivalence relations, Journal of the American Mathematical Society, vol. 3 (1990), pp. 663693.
[4]Hjorth, G., Countable models and the theory of Borel equivalence relations, Notre Dame Lecture Notes in Logic, vol. 18 (2005), pp. 143.
[5]Hjorth, G. and Kechris, A. S., Borel equivalence relations and classifications of countable models, Annals of Pure and Applied Logic, vol. 82 (1996), pp. 221272.
[6]Hjorth, G., Kechris, A. S., and Louveau, A., Borel equivalence relations induced by actions of the symmetric group, Annals of Pure and Applied Logic, vol. 92 (1998), pp. 63112.
[7]Hjorth, Greg and Kechris, Alexander, New dichotomies for borel equivalence relations, The Bulletin of Symbolic Logic, vol. 3 (1997), no. 3, pp. 329346.
[8]Jackson, S., Kechris, A. S., and Louveau, A., Countable Borel equivalence relations, Journal of Mathematical Logic, vol. 2 (2002), no. 1, pp. 180.
[9]Koerwien, M., La complexité de la relation d'isomorphisme pour les modèles dènombrables d'une théorie oméga-stable, Ph.D. thesis, Université Paris 7, 2007, available at
[10]Koerwien, M., Comparing borel reducibility and depth of an ω-stable theory, to appear.
[11]Lascar, D., Why some people are excited by vaught's conjecture, this Journal, vol. 50 (1985), pp. 973982.
[12]Louveau, A. and Velickovic, B., A note on Borel equivalence relations, Proceedings of the American Mathematical Society, vol. 120 (1994), pp. 255259.
[13]Shelah, S., Classification theory and the number of nonisomorphic models, North Holland, 1978.



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