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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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EF-equivalent not isomorphic pair of models
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by Saharon Shelah PDF
Proc. Amer. Math. Soc. 136 (2008), 4405-4412 Request permission


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.
  • Chanoch Havlin and Saharon Shelah, Existence of EF-equivalent non-isomorphic models, MLQ Math. Log. Q. 53 (2007), no. 2, 111–127. MR 2308491, DOI 10.1002/malq.200610031
  • Saharon Shelah. Theories with EF-Equivalent Non-isomorphic Models. Tbilisi Mathematical Journal, submitted. math.LO/0703477.
  • 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
  • Heikki Tuuri. Infinitary languages and Ehrenfeucht-Fraïssé games. Ph.D. thesis, University of Helsinki, 1990.
  • 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
  • MR Author ID: 160185
  • ORCID: 0000-0003-0462-3152
  • Email:
  • 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
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 4405-4412
  • MSC (2000): Primary 03C75
  • DOI:
  • MathSciNet review: 2431056