Nonmaximal decidable structures

Given any infinite structure with a decidable first-order theory, we give a sufficient condition in terms of the Gaifman graph of that ensures that can be expanded with some nondefinable predicate in such a way that the first-order theory of the expansion is still decidable. Bibliography: 10 titles.

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Veröffentlicht in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2009-05, Vol.158 (5), p.615-622
Hauptverfasser: Bès, A., Cégielski, P.
Format: Artikel
Sprache:eng
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Zusammenfassung:Given any infinite structure with a decidable first-order theory, we give a sufficient condition in terms of the Gaifman graph of that ensures that can be expanded with some nondefinable predicate in such a way that the first-order theory of the expansion is still decidable. Bibliography: 10 titles.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-009-9399-x