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Preprint Number 9

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9. O. Belegradek, B. Zilber
Definable relations in the real field with a distinguished subgroup of the unit circle

Submission date: 1 March 2006


We describe definable relations in the real field augmented by a binary relation which is an arbitrary multiplicative group of complex numbers contained in the divisible hull of a finitely generated subgroup of the unit circle. We give a complete axiom system for this structure which admits quantifier elimination down to Booleam combinations of existential formulas of a special simple form.

Mathematics Subject Classification: 03C60

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