Real Closed Exponential Subfields of Pseudoexponential Fields

摘要

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