Real Closed Exponential Subfields of Pseudoexponential Fields

TL;DR

This paper demonstrates that pseudoexponential fields contain continuum many non-isomorphic countable real closed exponential subfields with surjective exponential maps, extending to any algebraically closed exponential field satisfying Schanuel's conjecture.

Contribution

It establishes the abundance of real closed exponential subfields within pseudoexponential fields and related algebraically closed exponential fields under Schanuel's conjecture.

Findings

Existence of continuum many non-isomorphic countable real closed exponential subfields.

Each subfield has an order-preserving exponential map surjective onto nonnegative elements.

Results apply to any algebraically closed exponential field satisfying Schanuel's conjecture.

Abstract

In this paper, we prove that a pseudoexponential field has continuum many non-isomorphic countable real closed exponential subfields, each with an order preserving exponential map which is surjective onto the nonnegative elements. Indeed, this is true of any algebraically closed exponential field satisfying Schanuel's conjecture.