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The algebraic numbers definable in various exponential fields

  • Jonathan Kirby (a1), Angus Macintyre (a2) and Alf Onshuus (a3)

Abstract

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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The algebraic numbers definable in various exponential fields

  • Jonathan Kirby (a1), Angus Macintyre (a2) and Alf Onshuus (a3)

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