Hostname: page-component-848d4c4894-r5zm4 Total loading time: 0 Render date: 2024-06-23T03:07:14.173Z Has data issue: false hasContentIssue false

Interpreting second-order logic in the monadic theory of order1

Published online by Cambridge University Press:  12 March 2014

Yuri Gurevich*
Bowling Green University, Bowling Green, Ohio 43403
Saharon Shelah
Mathematics Institute, Hebrew University, Jerusalem, Israel
Department of Computer and Conmunication Sciences, University of Michigan, Ann Arbor, Michigan 48109


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

Research Article
Copyright © Association for Symbolic Logic 1983

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)



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.



[1]Gurevich, Y., Monadic theory of order and topology. II, Israel Journal of Mathematics, vol. 34(1979), pp. 4571.CrossRefGoogle Scholar
[2]Gurevich, Y., Monadic second-order theories, Abstract model theory and stronger logics (Barwise, J. and Feferman, S., Editors), Springer-Verlag, Berlin (to appear).Google Scholar
[3]Gurevich, Y. and Shelah, S., Monadic theory of order and topology in ZFC, Annals of Mathematical Logic (to appear).Google Scholar
[4]Jech, T. J., Set theory, Academic Press, New York, 1978.Google Scholar
[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.Google Scholar
[6]Shelah, S., The monadic theory of order, Annals of Mathematics, vol. 102 (1975), pp. 379419.CrossRefGoogle Scholar