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arXiv · 1101.4224

The algebraic numbers definable in various exponential fields

Jonathan Kirby·Angus Macintyre·Alf Onshuus
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Abstract

We prove the following theorems: Theorem 1: For any E-field with cyclic kernel, in particular $\mathbb C$ 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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Jonathan Kirby, Angus Macintyre, Alf Onshuus. 2011-01-21. The algebraic numbers definable in various exponential fields. https://doi.org/10.1017/s1474748012000047

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