The model theory of the field of reals with a subgroup of the unit circle

• Autores: Oleg Belegradek, Boris Zilber
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 78, Nº 3, 2008, págs. 563-579
• Idioma: inglés
• DOI: 10.1112/jlms/jdn037
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• Resumen

  • We describe definable sets in the field of reals augmented by a predicate for a finite rank multiplicative group of complex numbers contained in the unit circle . This structure interprets the quotient-space / which, for infinite cyclic, is related to the quantum torus. Every definable set is proved to be a Boolean combination of existentially definable sets. We give a complete set of axioms for the theory of such a structure