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| HAL : hal-00655411, version 1 |
| Fiche détaillée |  Récupérer au format |
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| Cédric Milliet 1, 2 |
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| (28/12/2011) |
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| We investigate some common points between stable and weakly small structures and define a structure M to be "fine" if the topological space S_\phi(dcl^{eq}(A)) has an ordinal Cantor-Bendixson rank for every formula phi and finite subset A of M. By definition, a theory is "fine" if every of its models is so. Weakly minimal, small, and stable structures are all examples of fine structures. For any of its finite subset A, a fine structure has local descending chain conditions on the algebraic closure acl(A) of A for subgroups uniformly definable over acl(A). An infinite field with fine theory has no additive or multiplicative proper subgroup of finite index, and no Artin-Schreier extension. |
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| 1 : | Institut Camille Jordan (ICJ) |
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CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon |
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| 2 : | Département de Mathématiques |
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Galatasaray Universitesi |
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| Domaine | : | Mathématiques/Logique |
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| théorie des modèles – rang de Cantor-Bendixson – condition de chaîne locale – extension d'Artin-Schreier |
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| hal-00655411, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00655411 | |
| oai:hal.archives-ouvertes.fr:hal-00655411 | |
| Contributeur : Cédric Milliet | |
| Soumis le : Mercredi 28 Décembre 2011, 17:02:38 | |
| Dernière modification le : Jeudi 29 Décembre 2011, 08:25:08 | |
