Notre Dame Journal of Formal Logic 54 (3-4):509-520 (2013)

Abstract
We show that Zilber’s conjecture that complex exponentiation is isomorphic to his pseudo-exponentiation follows from the a priori simpler conjecture that they are elementarily equivalent. An analysis of the first-order types in pseudo-exponentiation leads to a description of the elementary embeddings, and the result that pseudo-exponential fields are precisely the models of their common first-order theory which are atomic over exponential transcendence bases. We also show that the class of all pseudo-exponential fields is an example of a nonfinitary abstract elementary class, answering a question of Kesälä and Baldwin
Keywords pseudo-exponentiation   exponential fields   Schanuel property   first-order theory   abstract elementary class
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DOI 10.1215/00294527-2143844
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References found in this work BETA

Independence in Finitary Abstract Elementary Classes.Tapani Hyttinen & Meeri Kesälä - 2006 - Annals of Pure and Applied Logic 143 (1-3):103-138.
Abstract Elementary Classes and Infinitary Logics.David W. Kueker - 2008 - Annals of Pure and Applied Logic 156 (2):274-286.
Algebraically Closed Field with Pseudo-Exponentiation.B. Zilber - 2005 - Annals of Pure and Applied Logic 132 (1):67-95.

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Citations of this work BETA

Shelah's Eventual Categoricity Conjecture in Universal Classes: Part I.Sebastien Vasey - 2017 - Annals of Pure and Applied Logic 168 (9):1609-1642.
Abstract Elementary Classes Stable in ℵ 0.Saharon Shelah & Sebastien Vasey - 2018 - Annals of Pure and Applied Logic 169 (7):565-587.
Computable Categoricity for Pseudo-Exponential Fields of Sizeℵ1.Jesse Johnson - 2014 - Annals of Pure and Applied Logic 165 (7-8):1301-1317.
A Pseudoexponential-Like Structure on the Algebraic Numbers.Vincenzo Mantova - 2015 - Journal of Symbolic Logic 80 (4):1339-1347.
Adequate Predimension Inequalities in Differential Fields.Vahagn Aslanyan - 2022 - Annals of Pure and Applied Logic 173 (1):103030.

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