# Utilisation des destinées pour la décision et sa complexité dans le cas de formules à profondeur de quantification bornée sur des structures logiques finies et infinies

Abstract : We study finite or infinite logical structures, by considering the sets of sentences with quantifier depth $k$ that are true in these structures. More spacifically, we use a new logic tool called Nézondet destinies. A $k$-destiny of a structure is a tree containing all the $k$-isomorphism types of the structure. We show that destinies are a very relevant notion, equivalent to Fraïssé $k$-isomorphism and Ehrenfeucht games.

We present a decision algorithm using destinies. We carefully compare the class of structures for which there exists an algorithm to construct destinies, and the class of $H$-bounded structures. Finally, we give some partial results on the NE vs. CoNE problem and its logic equivalent, the Spectrum conjecture
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https://tel.archives-ouvertes.fr/tel-00011983
Contributor : Annie Chateau <>
Submitted on : Monday, March 20, 2006 - 12:35:58 AM
Last modification on : Wednesday, April 17, 2019 - 3:28:05 PM
Long-term archiving on : Monday, September 17, 2012 - 12:45:22 PM

### Identifiers

• HAL Id : tel-00011983, version 1

### Citation

Annie Chateau. Utilisation des destinées pour la décision et sa complexité dans le cas de formules à profondeur de quantification bornée sur des structures logiques finies et infinies. Mathématiques [math]. Université d'Auvergne - Clermont-Ferrand I, 2003. Français. ⟨tel-00011983⟩

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