In this paper, we prove that a pseudo-exponential field has continuum many nonisomorphic 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.
- Exponential algebra
- Real closed exponential fields
- Schanuel's conjecture
ASJC Scopus subject areas