21 found
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  1.  4
    Definable Types in Algebraically Closed Valued Fields.Pablo Cubides Kovacsics & Françoise Delon - 2016 - Mathematical Logic Quarterly 62 (1-2):35-45.
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  2.  3
    The Theory of Modules of Separably Closed Fields 2.Pilar Dellunde, Françoise Delon & Françoise Point - 2004 - Annals of Pure and Applied Logic 129 (1-3):181-210.
    In Dellunde et al. 997–1015), we determined the complete theory Te of modules of separably closed fields of characteristic p and imperfection degree e, eω{∞}. Here, for 0≠eω, we describe the closed set of the Ziegler spectrum corresponding to Te. Further, we establish a correspondence between certain submodules and n-types and we investigate several notions of dimensions and their relationships with the Lascar rank. Finally, we show that Te has uniform p.p. elimination of imaginaries and deduce uniform weak elimination of (...)
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  3. Extensions Séparées Et Immédiates de Corps Valués.Françoise Delon - 1988 - Journal of Symbolic Logic 53 (2):421-428.
    Separated and immediate extensions of valued fields. The notion of separated extension of valued fields was introduced by Baur. He showed that extensions of maximal fields are separated. We prove that, when (K, v) is Henselian with residual characteristic 0, then $(K, v) \subset (L, w)$ is separated iff L is linearly disjoint over K from each immediate extension of K.
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  4.  18
    Inclusions Et Produits de Groupes Abéliens Ordonnés Étudiés au Premier Ordre.Françoise Delon & François Lucas - 1989 - Journal of Symbolic Logic 54 (2):499-511.
  5.  26
    Some Model Theory for Almost Real Closed Fields.Françoise Delon & Rafel Farré - 1996 - Journal of Symbolic Logic 61 (4):1121-1152.
    We study the model theory of fields k carrying a henselian valuation with real closed residue field. We give a criteria for elementary equivalence and elementary inclusion of such fields involving the value group of a not necessarily definable valuation. This allows us to translate theories of such fields to theories of ordered abelian groups, and we study the properties of this translation. We also characterize the first-order definable convex subgroups of a given ordered abelian group and prove that the (...)
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  6.  10
    Plongement Dense d'Un Corps Ordonné Dans Sa Clôture Réelle.Françoise Delon - 1991 - Journal of Symbolic Logic 56 (3):974-980.
    We study the structures $(K \subset K^\mathrm{r})$ , where K is an ordered field and Kr its real closure, in the language of ordered fields with an additional unary predicate for the subfield K. Two such structures $(K \subset K^\mathrm{r})$ and $(L \subset L^\mathrm{r})$ are not necessarily elementary equivalent when K and L are. But with some saturation assumption on K and L, then the two structures become equivalent, and we give a description of the complete theory.
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  7.  16
    Alexander Prestel. Einführung in die mathematische Logik und Modelltheorie. Vieweg studium, no. 60. Friedr. Vieweg & Sohn, Brunswick et Wiesbaden 1986, xiv + 286 pp. [REVIEW]Francoise Delon - 1991 - Journal of Symbolic Logic 56 (1):341-343.
  8.  32
    Corps Portant Un Nombre Fini de Valuations.Françoise Delon - 1987 - Journal of Symbolic Logic 52 (4):994-1004.
    L. van den Dries proved that the theory of n-valued rings has a model companion. We show here that this result is still true when the valuation rings are required to satisfy given inclusion relations (we restrict ourselves to the case of residual characteristic zero).
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  9.  10
    Extensions Separees Et Immediates de Corps Values.Francoise Delon - 1988 - Journal of Symbolic Logic 53 (2):421-428.
    Separated and immediate extensions of valued fields. The notion of separated extension of valued fields was introduced by Baur. He showed that extensions of maximal fields are separated. We prove that, when $(K, v)$ is Henselian with residual characteristic 0, then $(K, v) \subset (L, w)$ is separated iff $L$ is linearly disjoint over $K$ from each immediate extension of $K$.
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  10.  20
    Espaces Ultramétriques.Françoise Delon - 1984 - Journal of Symbolic Logic 49 (2):405-424.
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  11.  14
    Indécidabilité de Corps de Séries Formelles.Françoise Delon & Yamina Rouani - 1988 - Journal of Symbolic Logic 53 (4):1227-1234.
    Consider k((G)) in the language of valued fields enriched with a unary predicate for the set of constants and another one for the cross-section. For perfect k, this structure is undecidable if it does not satisfy Kaplansky's conditions.
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  12.  9
    Indecidabilite de la Theorie Des Paires Immediates de Corps Values Henseliens.Françoise Delon - 1991 - Journal of Symbolic Logic 56 (4):1236-1242.
    The theory of immediate pairs of Henselian valued fields, with a given residual theory (of characteristic zero) and a given theory of valuation group (nonzero), is undecidable and has 2ℵ0 completions.
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  13. Plongement Dense d'un Corps Ordonne dans sa Cloture Reelle.Françoise Delon - 1991 - Journal of Symbolic Logic 56 (3):974-980.
    We study the structures $$, where $K$ is an ordered field and $K^\mathrm{r}$ its real closure, in the language of ordered fields with an additional unary predicate for the subfield $K$. Two such structures $$ and $$ are not necessarily elementary equivalent when $K$ and $L$ are. But with some saturation assumption on $K$ and $L$, then the two structures become equivalent, and we give a description of the complete theory.
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  14.  8
    Periodicite Des Theories Elementaires Des Corps De Series Formelles Iterees.Françoise Delon - 1986 - Journal of Symbolic Logic 51 (2):334-351.
    C. U. Jensen suggested the following construction, starting from a field $K: K_0 = K, K_{\alpha + 1} = K_\alpha ((X_\alpha)), K_\alpha = \bigcup K_\beta$ if $\alpha$ is limit and asked when two fields $k_\alpha$ and $K_\beta$ are equivalent. We give a complete answer in the case of a field $K$ of characteristic 0.
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  15.  22
    Périodicité des Théories Élémentaires des Corps de Séries Formelles Itérées.Françoise Delon - 1986 - Journal of Symbolic Logic 51 (2):334-351.
    C. U. Jensen suggested the following construction, starting from a fieldK:and asked when two fieldsKαandKβare equivalent. We give a complete answer in the case of a fieldKof characteristic 0.
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  16.  6
    The Undecidability of the Theory of Immediate Pairs of Henselian Valued Fields.Françoise Delon - 1991 - Journal of Symbolic Logic 56 (4):1236-1242.
  17.  23
    Un Principe d'Ax-Kochen-Ershov Pour Des Structures Intermediares Entre Groupes Et Corps Values.Françoise Delon & Patrick Simonetta - 1999 - Journal of Symbolic Logic 64 (3):991-1027.
    An Ax-Kochen-Ershov principle for intermediate structures between valued groups and valued fields. We will consider structures that we call valued B-groups and which are of the form $\langle G, B, *, v\rangle$ where - G is an abelian group, - B is an ordered group, - v is a valuation defined on G taking its values in B, - * is an action of B on G satisfying: ∀ x ∈ G ∀ b ∈ B v(x * b) = v(x) (...)
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  18. Undecidable Wreath Products and Skew Power Series Fields.Françoise Delon & Patrick Simonetta - 1998 - Journal of Symbolic Logic 63 (1):237-246.
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  19. XVIIème Problème de Hilbert Sur Les Corps Chaîne-Clos.Françoise Delon & Danielle Gondard - 1991 - Journal of Symbolic Logic 56 (3):853-861.
    A chain-closed field is defined as a chainable field (i.e. a real field such that, for all n ∈ N, Σ K2n+1 ≠ Σ K2n) which does not admit any "faithful" algebraic extension, and can also be seen as a field having a Henselian valuation ν such that the residue field K/ν is real closed and the value group ν K is odd divisible with |ν K/2ν K| = 2. If K admits only one such valuation, we show that f (...)
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  20.  7
    XVIIeme Probleme de Hilbert sur les Corps Chaine-Clos.Francoise Delon & Danielle Gondard - 1991 - Journal of Symbolic Logic 56 (3):853.
    A chain-closed field is defined as a chainable field which does not admit any "faithful" algebraic extension, and can also be seen as a field having a Henselian valuation $\nu$ such that the residue field $K/\nu$ is real closed and the value group $\nu K$ is odd divisible with $|\nu K/2\nu K| = 2$. If $K$ admits only one such valuation, we show that $f \in K$ is in $\mathbf{\Sigma} K^{2n} \operatorname{iff}$ for any real algebraic extension $L$ of $K, "f (...)
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  21.  20
    Une Fonction de Kolchin Pour les Corps Imparfaits de Degré d'Imperfection Fini.Françoise Delon - 2005 - Journal of Symbolic Logic 70 (2):664 - 680.
    Non-perfect separably closed fields are stable, and not superstable. As a result, not all types can be ranked. We develop here a new tool, a "semi-rank", which takes values in the non-negative reals, and gives a sufficient condition for forking of types. This semi-rank is built up from a transcendence function, analogous to the one considered by Kolchin in the context of differentially closed fields. It yields some orthogonality and stratification results. /// Un corps séparablement clos non algébriquement clos est (...)
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