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Weakly maximal decidable structures

  • Alexis Bès (a1) and Patrick Cégielski (a1)


We prove that there exists a structure M whose monadic second order theory is decidable, and such that the first-order theory of every expansion of M by a constant is undecidable. 



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[1] J.R. Büchi, On a decision method in the restricted second-order arithmetic. In Proc. Int. Congress Logic, Methodology and Philosophy of science, Berkeley 1960. Stanford University Press (1962) 1–11.
[2] K.J. Compton, On rich words. In M. Lothaire, editor, Combinatorics on words. Progress and perspectives, Proc. Int. Meet., Waterloo, Canada (1982). Encyclopedia of Mathematics 17, Addison-Wesley (1983) 39–61.
[3] C.C. Elgot and M.O. Rabin. Decidability and undecidability of extensions of second (first) order theory of (generalized) successor. J. Symbolic Logic 31 (1966) 169–181.
[4] Feferman, S. and Vaught, R.L., The first order properties of products of algebraic systems. Fund. Math. 47 (1959) 57103.
[5] D. Perrin and J.-É. Pin, Infinite Words. Pure Appl. Math. 141 (2004).
[6] Harizanov, V.S., Computably-theoretic complexity of countable structures. Bull. Symbolic Logic 8 (2002) 457477.
[7] Shelah, S., The monadic theory of order. Ann. Math. 102 (1975) 379419.
[8] Soprunov, S., Decidable expansions of structures. Vopr. Kibern. 134 (1988) 175179 (in Russian).
[9] Thomas, W., The theory of successor with an extra predicate. Math. Ann. 237 (1978) 121132.
[10] Thomas, W., Ehrenfeucht games, the composition method, and the monadic theory of ordinal words. In Structures in Logic and Computer Science, A Selection of Essays in Honor of A. Ehrenfeucht. Lect. Notes Comput. Sci. 1261 (1997) 118143.


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Weakly maximal decidable structures

  • Alexis Bès (a1) and Patrick Cégielski (a1)


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