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2021-01-01 - Article/Compte-rendu - Anglais - page(s) (A publier)

Mariaule Nathanael , "Expansion of Presburger arithmetic with the Exchange Property" in Mathematical Logic Quarterly

  • Edition : John Wiley & Sons (United Kingdom)
  • Codes CREF : Logique mathématique (DI1170)
  • Unités de recherche UMONS : Logique mathématique (S838)
  • Instituts UMONS : Institut de Recherche sur les Systèmes Complexes (Complexys)
Texte intégral :

Abstract(s) :

(Anglais) Let G be a model of Presburger arithmetic. Let L be an expansion of the language of Presburger L_Pres. In this paper, we prove that the L-theory of G is L_Pres-minimal iff it has the exchange property and is definably complete (i.e., any bounded definable set has a maximum). If the L-theory of G has the exchange but is not definably complete, there is a proper definable convex subgroup H. Assuming that the induced theories on H and G/H are definable complete and o-minimal resp., we prove that any definable set of G is L_PresU{H}-definable


Mots-clés :
  • (Anglais) Presburger arithmetic
  • (Anglais) minimality
  • (Anglais) exchange property