24 found
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  1.  35
    Topological Differential Fields.Nicolas Guzy & Françoise Point - 2010 - Annals of Pure and Applied Logic 161 (4):570-598.
    We consider first-order theories of topological fields admitting a model-completion and their expansion to differential fields . We give a criterion under which the expansion still admits a model-completion which we axiomatize. It generalizes previous results due to M. Singer for ordered differential fields and of C. Michaux for valued differential fields. As a corollary, we show a transfer result for the NIP property. We also give a geometrical axiomatization of that model-completion. Then, for certain differential valued fields, we extend (...)
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  2.  16
    Existentially Closed Ordered Difference Fields and Rings.Françoise Point - 2010 - Mathematical Logic Quarterly 56 (3):239-256.
    We describe classes of existentially closed ordered difference fields and rings. We show an Ax-Kochen type result for a class of valued ordered difference fields.
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  3.  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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  4.  30
    Topological Differential Fields and Dimension Functions.Nicolas Guzy & Françoise Point - 2012 - Journal of Symbolic Logic 77 (4):1147-1164.
    We construct a fibered dimension function in some topological differential fields.
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  5.  6
    Essentially Periodic Ordered Groups.Françoise Point & Frank O. Wagner - 2000 - Annals of Pure and Applied Logic 105 (1-3):261-291.
    A totally ordered group G is essentially periodic if for every definable non-trivial convex subgroup H of G every definable subset of G is equal to a finite union of cosets of subgroups of G on some interval containing an end segment of H; it is coset-minimal if all definable subsets are equal to a finite union of cosets, intersected with intervals. We study definable sets and functions in such groups, and relate them to the quasi-o-minimal groups introduced in Belegradek (...)
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  6.  3
    Strong Density of Definable Types and Closed Ordered Differential Fields.Quentin Brouette, Pablo Cubides Kovacsics & Françoise Point - 2019 - Journal of Symbolic Logic 84 (3):1099-1117.
    The following strong form of density of definable types is introduced for theories T admitting a fibered dimension function d: given a model M of T and a definable set X ⊆ Mn, there is a definable type p in X, definable over a code for X and of the same d-dimension as X. Both o-minimal theories and the theory of closed ordered differential fields are shown to have this property. As an application, we derive a new proof of elimination (...)
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  7.  10
    Ultraproducts and Chevalley Groups.Françoise Point - 1999 - Archive for Mathematical Logic 38 (6):355-372.
    Given a simple non-trivial finite-dimensional Lie algebra L, fields $K_i$ and Chevalley groups $L(K_i)$ , we first prove that $\Pi_{\mathcal{U}} L(K_i)$ is isomorphic to $L(\Pi_{\mathcal{U}}K_i)$ . Then we consider the case of Chevalley groups of twisted type ${}^n\!L$ . We obtain a result analogous to the previous one. Given perfect fields $K_i$ having the property that any element is either a square or the opposite of a square and Chevalley groups ${}^n\!L(K_i)$ , then $\pu{}^n\!L(K_i)$ is isomorphic to ${}^n\!L(\pu K_i)$ . (...)
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  8.  10
    Free Abelian Lattice-Ordered Groups.A. M. W. Glass, Angus Macintyre & Françoise Point - 2005 - Annals of Pure and Applied Logic 134 (2-3):265-283.
    Let n be a positive integer and FAℓ be the free abelian lattice-ordered group on n generators. We prove that FAℓ and FAℓ do not satisfy the same first-order sentences in the language if m≠n. We also show that is decidable iff n{1,2}. Finally, we apply a similar analysis and get analogous results for the free finitely generated vector lattices.
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  9.  3
    The Ziegler Spectrum of the Ring of Entire Complex Valued Functions.Sonia L’Innocente, Françoise Point, Gena Puninski & Carlo Toffalori - 2019 - Journal of Symbolic Logic 84 (1):160-177.
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  10.  7
    Quantifier Elimination in Discriminator Varieties.Francoise Point - 1986 - Annals of Pure and Applied Logic 32 (1):83-101.
  11.  8
    Definability of Types and VC Density in Differential Topological Fields.Françoise Point - 2018 - Archive for Mathematical Logic 57 (7-8):809-828.
    Given a model-complete theory of topological fields, we considered its generic differential expansions and under a certain hypothesis of largeness, we axiomatised the class of existentially closed ones. Here we show that a density result for definable types over definably closed subsets in such differential topological fields. Then we show two transfer results, one on the VC-density and the other one, on the combinatorial property NTP2.
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  12.  33
    Quantifier Elimination in Valued Ore Modules.Luc Bélair & Françoise Point - 2010 - Journal of Symbolic Logic 75 (3):1007-1034.
    We consider valued fields with a distinguished isometry or contractive derivation as valued modules over the Ore ring of difference operators. Under certain assumptions on the residue field, we prove quantifier elimination first in the pure module language, then in that language augmented with a chain of additive subgroups, and finally in a two-sorted language with a valuation map. We apply quantifier elimination to prove that these structures do not have the independence property.
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  13.  14
    Erratum to “Free Abelian Lattice-Ordered Groups” [Ann. Pure Appl. Logic 134 265–283].A. M. W. Glass, Angus Macintyre & Françoise Point - 2016 - Annals of Pure and Applied Logic 167 (4):431-433.
  14.  4
    On Differential Galois Groups of Strongly Normal Extensions.Quentin Brouette & Françoise Point - 2018 - Mathematical Logic Quarterly 64 (3):155-169.
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  15.  12
    Finitely Generic Models of tUH, for Certain Model Companionable Theories T.Francoise Point - 1985 - Journal of Symbolic Logic 50 (3):604 - 610.
  16.  13
    Asymptotic Theory of Modules of Separably Closed Fields.Françoise Point - 2005 - Journal of Symbolic Logic 70 (2):573-592.
    We consider the reduct to the module language of certain theories of fields with a non surjective endomorphism. We show in some cases the existence of a model companion. We apply our results for axiomatizing the reduct to the theory of modules of non principal ultraproducts of separably closed fields of fixed but non zero imperfection degree.
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  17.  13
    Corrigendum To: “Quantifier Elimination in Valued Ore Modules”.Luc Bélair & Françoise Point - 2012 - Journal of Symbolic Logic 77 (2):727-728.
  18. Definability in Valued Ore Modules.Françoise Point - forthcoming - Bulletin of Symbolic Logic.
  19.  10
    Phoenix Civic Plaza, Phoenix, Arizona, January 9–10, 2004.Matthew Foreman, Steve Jackson, Julia Knight, R. W. Knight, Steffen Lempp, Françoise Point, Kobi Peterzil, Leonard Schulman, Slawomir Solecki & Carol Wood - 2004 - Bulletin of Symbolic Logic 10 (2).
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  20.  5
    Corrigendum toF. Point, Existentially Closed Ordered Difference Fields and Rings.Françoise Point - 2015 - Mathematical Logic Quarterly 61 (1-2):117-119.
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  21.  2
    Separably Closed Fields and Contractive Ore Modules.Luc Bélair & Françoise Point - 2015 - Journal of Symbolic Logic 80 (4):1315-1338.
  22. On Decidable Extensions of Presburger Arithmetic: From A. Bertrand Numeration Systems to Pisot Numbers.Françoise Point - 2000 - Journal of Symbolic Logic 65 (3):1347-1374.
    We study extensions of Presburger arithmetic with a unary predicate R and we show that under certain conditions on R, R is sparse and the theory of $\langle\mathbb{N}, +, R\rangle$ is decidable. We axiomatize this theory and we show that in a reasonable language, it admits quantifier elimination. We obtain similar results for the structure $\langle\mathbb{Q},+, R\rangle$.
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  23.  48
    The Theory of Modules of Separably Closed Fields. I.Pilar Dellunde, Françoise Delon & Françoise Point - 2002 - Journal of Symbolic Logic 67 (3):997-1015.
    We consider separably closed fields of characteristic $p > 0$ and fixed imperfection degree as modules over a skew polynomial ring. We axiomatize the corresponding theory and we show that it is complete and that it admits quantifier elimination in the usual module language augmented with additive functions which are the analog of the $p$-component functions.
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  24.  16
    Exponentiations Over the Universal Enveloping Algebra of s L 2.Sonia L’Innocente, Angus Macintyre & Françoise Point - 2010 - Annals of Pure and Applied Logic 161 (12):1565-1580.
    We construct, by model-theoretic methods, several exponentiations on the universal enveloping algebra U of the Lie algebra.
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