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schanuel conjecture

Journal of the Institute of Mathematics of Jussieu (1)

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1 results

The algebraic numbers definable in various exponential fields
Part of
- Model theory
- Number theory: Connections with logic
Jonathan Kirby, Angus Macintyre, Alf Onshuus
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 11 / Issue 4 / October 2012

Published online by Cambridge University Press:

02 April 2012, pp. 825-834

Print publication:

October 2012
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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.