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2020-11-25 - Colloque/Présentation - communication orale - Anglais - 33 page(s)

Point Françoise , "Generic differential expansions of topological fields of characteristic 0" in Mathematical Science Research Institute, Berkeley, Etats-Unis, 2020

  • Codes CREF : Algèbre - théorie des anneaux - théorie des corps (DI1147), Logique mathématique (DI1170)
  • Unités de recherche UMONS : Logique mathématique (S838)
  • Instituts UMONS : Institut de Recherche sur les Systèmes Complexes (Complexys)
  • Centres UMONS : Algèbre, Géométrie et Interactions fondamentales (AGIF)
Texte intégral :

Abstract(s) :

(Anglais) Given a complete theory T of henselian valued fields of characteristic 0, we axiomatize the class of existentially closed differential expansions of models of T. Let us denote this axiomatization by T_\delta^*. Then we examine which model-theoretic properties transfer from T to T_\delta^* such as the existence of a dimension function on definable sets, or the existence of a code for definable sets (elimination of imaginaries). The main technical tool is a cell decomposition theorem for models of T and a description of definable functions (and more generally correspondences). (This is the analog in this setting of a result of P. Simon and E. Walsberg for dp-minimal, non strongly minimal fields of characteristic 0). Then we illustrate why this set-up is convenient to look at dense pairs of models of T. This is joint work with Nicolas Guzy and Pablo Cubidès.