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Preprint Number 289

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289. Jonathan Kirby, Angus Macintyre, and Alf Onshuus
The algebraic numbers definable in various exponential fields

Submission date: 21 January 2011.


We prove the following theorems:
Theorem 1: For any E-field with cyclic kernel, in particular C or the Zilber fields, all real abelian algebraic numbers are pointwise definable.
Theorem 2: For the Zilber fields, the only pointwise definable algebraic numbers are the real abelian numbers.

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