The algebraic numbers definable in various exponential fields

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.

References in corpus (3)

• On Quasiminimal Excellent Classes
• Exponential algebraicity in exponential fields
• A note on the axioms for Zilber's pseudo-exponential fields

Cited by in corpus (2)

• Finitely Presented Exponential Fields
• Algebraic types in Zilber's exponential field