Henson and Rubel's Theorem for Zilber's Pseudoexponentiation

TL;DR

This paper provides an alternative proof of the Schanuel Nullstellensatz for Zilber's Pseudoexponentiation and explores conditions under which exponential algebraic closure follows from algebraic closure in certain exponential fields.

Contribution

It offers a new proof of a key theorem in exponential algebra and clarifies the relationship between exponential algebraic closure and algebraic closure in specific fields.

Findings

Alternative proof of Schanuel Nullstellensatz for Zilber's Pseudoexponentiation

Exponential algebraic closure follows from algebraic closure in certain surjective exponential fields

Conditions for exponential algebraic closure in algebraically closed exponential fields

Abstract

This paper contains an alternate proof of the Schanuel Nullstellensatz for Zilber's Pseudoexponentiation. Furthermore, in an algebraically closed exponential field whose exponential map is surjective with standard kernel, this property follows from the field being exponentially algebraically closed.