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2009-05-01 - Article/Dans un journal avec peer-review - Anglais - 18 page(s)

Brihaye Thomas , Michaux Christian , Rivière Cédric , "Cell decomposition and dimension function in the theory of closed ordered differential fields" in Annals of Pure & Applied Logic, 159, Issues 1-2, 111-128

  • Edition : Elsevier Science
  • Codes CREF : Théorie des nombres (DI1141), Logique mathématique (DI1170), Géométrie algébrique (DI1111)
  • Unités de recherche UMONS : Mathématiques effectives (S820), Logique mathématique (S838), Géométrie algébrique (S843)
Texte intégral :

Abstract(s) :

(Anglais) 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 (called d-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.

Identifiants :
  • DOI : 10.1016/j.apal.2008.09.029