Notre Dame Journal of Formal Logic 54 (3-4):591-601 (2013)

Abstract
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
Keywords pseudo-exponential   exponential algebra   real closed exponential fields   Schanuel’s conjecture
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DOI 10.1215/00294527-2143925
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References found in this work BETA

Algebraically Closed Field with Pseudo-Exponentiation.B. Zilber - 2005 - Annals of Pure and Applied Logic 132 (1):67-95.
Schanuel's Conjecture and Free Exponential Rings.Angus Macintyre - 1991 - Annals of Pure and Applied Logic 51 (3):241-246.
A Remark on Zilber's Pseudoexponentiation.David Marker - 2006 - Journal of Symbolic Logic 71 (3):791 - 798.

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