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EF-equivalent not isomorphic pair of models

Author: Saharon Shelah
Journal: Proc. Amer. Math. Soc. 136 (2008), 4405-4412
MSC (2000): Primary 03C75
Published electronically: August 4, 2008
MathSciNet review: 2431056
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Abstract: We construct non-isomorphic models $ M,N$, e.g. of cardinality $ \aleph_1$, such that in the Ehrenfeucht-Fraissé game of any length $ \zeta < \omega_1$ the isomorphism player wins.

References [Enhancements On Off] (What's this?)

  • [HvSh 866] Chanoch Havlin and Saharon Shelah, Existence of EF-equivalent non-isomorphic models, MLQ Math. Log. Q. 53 (2007), no. 2, 111–127. MR 2308491,
  • [Sh 897] Saharon Shelah.
    Theories with EF-Equivalent Non-isomorphic Models.
    Tbilisi Mathematical Journal, submitted.
  • [Sh 836] Saharon Shelah, On long EF-equivalence in non-isomorphic models, Logic Colloquium ’03, Lect. Notes Log., vol. 24, Assoc. Symbol. Logic, La Jolla, CA, 2006, pp. 315–325. MR 2207360
  • [Tur90] Heikki Tuuri.
    Infinitary languages and Ehrenfeucht-Fraïssé games.
    Ph.D. thesis, University of Helsinki, 1990.
  • [Va95] Jouko Väänänen.
    Games and trees in infinitary logic: A survey.
    In M. Mostowski M. Krynicki and L. Szczerba, editors, Quantifiers, pages 105-138. Kluwer, 1995.

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Additional Information

Saharon Shelah
Affiliation: Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem 91904, Israel – and – Department of Mathematics, Hill Center, Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019

Received by editor(s): May 29, 2007
Received by editor(s) in revised form: September 11, 2007, and September 25, 2007
Published electronically: August 4, 2008
Additional Notes: The author’s research was supported by the German-Israeli Foundation for Scientific Research and Development (Grant No. I-706-54.6/2001). Publication 907
Communicated by: Julia Knight
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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