Séminaires : Séminaire de Logique Lyon-Paris

Equipe(s) : lm,
Responsables :S. Anscombe, O. Finkel, A. Khélif, S. Rideau, T. Tsankov, A. Vignati
Email des responsables :
Salle : Contacter Silvain Rideau ou Alessandro Vignati
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Orateur(s) Hector Pasten - PUC Chile,
Titre Diophantine sets of number fields and their rings of integers --- à 16h en salle 1016
Horaire16:00 à 17:00
RésumeA subset of a ring is diophantine if it is positive existentially definable in the language of rings. In number fields or in their rings of integers, every diophantine set is listable (i.e. recursively enumerable) and one can ask whether every listable set is diophantine. For instance, a classical theorem of Davis, Matiyasevic, Putnam, and Robinson shows that for the usual integers Z the answer is positive. I will discuss some general conjectures and some partial results suggesting that in the number field case not every listable set is diophantine, while in the case of rings of integers every listable set should be diophantine.

SalleContacter Silvain Rideau ou Alessandro Vignati