The Field of Reals is not omega-Automatic

Faried Abu Zaid , Erich Grädel (1) , Lukasz Kaiser (1)

1 Mathematische Grundlagen der Informatik

We investigate structural properties of omega-automatic presentations of infinite structures in order to sharpen our methods to determine whether a given structure is omega-automatic. We apply these methods to show that no field of characteristic 0 admits an injective omega-automatic presentation, and that uncountable fields with a definable linear order cannot be omega-automatic.

Mots clés: Logic; Algorithmic Model Theory; Automatic Structures

Domaines: Complexité [cs.CC]; Algorithme et structure de données [cs.DS]

Faried Abu Zaid, Erich Grädel, Lukasz Kaiser. The Field of Reals is not omega-Automatic. STACS'12 (29th Symposium on Theoretical Aspects of Computer Science), Feb 2012, Paris, France. pp.577-588. ⟨hal-00678194⟩