no. 1
Weakly maximal decidable structures
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 1, pp. 137-145.

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.

DOI : 10.1051/ita:2007044
Classification : 03B25, 03C57, 03D05
Mots clés : decidability, first-order theories, monadic second-order theories, maximality, automata, rich words 
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     title = {Weakly maximal decidable structures},
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Bès, Alexis; Cégielski, Patrick. Weakly maximal decidable structures. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 1, pp. 137-145. doi : 10.1051/ita:2007044. http://www.numdam.org/articles/10.1051/ita:2007044/

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