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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Weak Ehrenfeucht-Fraïssé games


Authors: Tapani Hyttinen and Vadim Kulikov
Journal: Trans. Amer. Math. Soc. 363 (2011), 3309-3334
MSC (2010): Primary 03C55; Secondary 03C52
Published electronically: January 11, 2011
MathSciNet review: 2775809
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Abstract: In this paper we define a game which is played between two players $ \textbf{I}$ and $ \textbf{II}$ and two mathematical structures $ \mathcal{A}$ and $ \mathcal{B}$. The players choose elements from both structures in $ \alpha$ moves, and at the end of the game player $ \textbf{II}$ wins if the chosen structures are isomorphic. Thus the difference between this and the ordinary Ehrenfeucht-Fraïssé game is that the isomorphism can be arbitrary, whereas in the ordinary EF-game it is determined by the moves of the players. We investigate determinacy of the weak EF-game for different $ \alpha$ (the length of the game) and its relation to the ordinary EF-game.


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Additional Information

Tapani Hyttinen
Affiliation: Department of Mathematics, University of Helsinki, P.O. Box 68 (Gustav Hällströmin katu 2b) FI-00014 Finland

Vadim Kulikov
Affiliation: Department of Mathematics, University of Helsinki, P.O. Box 68 (Gustav Hällströmin katu 2b) FI-00014 Finland

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05222-0
PII: S 0002-9947(2011)05222-0
Received by editor(s): October 17, 2008
Received by editor(s) in revised form: October 11, 2009
Published electronically: January 11, 2011
Additional Notes: The first author was partially supported by the Academy of Finland, grant 1106753
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.