4 found
Order:
  1. Geometrical Axiomatization for Model Complete Theories of Differential Topological Fields.Nicolas Guzy & Cédric Rivière - 2006 - Notre Dame Journal of Formal Logic 47 (3):331-341.
    In this paper we give a differential lifting principle which provides a general method to geometrically axiomatize the model companion (if it exists) of some theories of differential topological fields. The topological fields we consider here are in fact topological systems in the sense of van den Dries, and the lifting principle we develop is a generalization of the geometric axiomatization of the theory DCF₀ given by Pierce and Pillay. Moreover, it provides a geometric alternative to the axiomatizations obtained by (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  2.  6
    Cell Decomposition and Dimension Function in the Theory of Closed Ordered Differential Fields.Thomas Brihaye, Christian Michaux & Cédric Rivière - 2009 - Annals of Pure and Applied Logic 159 (1-2):111-128.
    In this paper we develop a differential analogue of o-minimal cell decomposition for the theory CODF of closed ordered differential fields. Thanks to this differential cell decomposition we define a well-behaving dimension function on the class of definable sets in CODF. We conclude this paper by proving that this dimension is closely related to both the usual differential transcendence degree and the topological dimension associated, in this case, with a natural differential topology on ordered differential fields.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  3. The Model Theory of M‐Ordered Differential Fields.Cédric Rivière - 2006 - Mathematical Logic Quarterly 52 (4):331-339.
    In his Ph.D. thesis [7], L. van den Dries studied the model theory of fields with finitely many orderings and valuations where all open sets according to the topology defined by an order or a valuation is globally dense according with all other orderings and valuations. Van den Dries proved that the theory of these fields is companionable and that the theory of the companion is decidable .In this paper we study the case where the fields are expanded with finitely (...))
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  4.  14
    Further Notes on Cell Decomposition in Closed Ordered Differential Fields.Cédric Rivière - 2009 - Annals of Pure and Applied Logic 159 (1-2):100-110.
    In [T. Brihaye, C. Michaux, C. Rivière, Cell decomposition and dimension function in the theory of closed ordered differential fields, Ann. Pure Appl. Logic .] the authors proved a cell decomposition theorem for the theory of closed ordered differential fields which generalizes the usual Cell Decomposition Theorem for o-minimal structures. As a consequence of this result, a well-behaving dimension function on definable sets in CODF was introduced. Here we continue the study of this cell decomposition in CODF by proving three (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   2 citations