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Interpreting second-order logic in the monadic theory of order1

  • Yuri Gurevich (a1) and Saharon Shelah (a2)


Under a weak set-theoretic assumption we interpret second-order logic in the monadic theory of order.


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Department of Computer and Conmunication Sciences, University of Michigan, Ann Arbor, Michigan 48109


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This work was done in principle during the 1980–81 academic year when both authors were fellows in the Institute for Advanced Studies of the Hebrew University in Jerusalem.



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[1]Gurevich, Y., Monadic theory of order and topology. II, Israel Journal of Mathematics, vol. 34(1979), pp. 4571.
[2]Gurevich, Y., Monadic second-order theories, Abstract model theory and stronger logics (Barwise, J. and Feferman, S., Editors), Springer-Verlag, Berlin (to appear).
[3]Gurevich, Y. and Shelah, S., Monadic theory of order and topology in ZFC, Annals of Mathematical Logic (to appear).
[4]Jech, T. J., Set theory, Academic Press, New York, 1978.
[5]Rabin, M.O., Decidability of second-order theories and automata on infinite trees, Transactions of the American Mathematical Society, vol. 141 (1969), pp. 135.
[6]Shelah, S., The monadic theory of order, Annals of Mathematics, vol. 102 (1975), pp. 379419.


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