The algebraic numbers definable in various exponential fields
Logic
2014-10-28 v1 Number Theory
Abstract
We prove the following theorems: Theorem 1: For any E-field with cyclic kernel, in particular 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.
Cite
@article{arxiv.1101.4224,
title = {The algebraic numbers definable in various exponential fields},
author = {Jonathan Kirby and Angus Macintyre and Alf Onshuus},
journal= {arXiv preprint arXiv:1101.4224},
year = {2014}
}