English

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 C\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.

Keywords

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}
}
R2 v1 2026-06-21T17:15:13.157Z