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 : https://doi.org/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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author = {B\es, Alexis and C\'egielski, Patrick},
title = {Weakly maximal decidable structures},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {137--145},
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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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