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2013 A Note on the Axioms for Zilber’s Pseudo-Exponential Fields
Jonathan Kirby
Notre Dame J. Formal Logic 54(3-4): 509-520 (2013). DOI: 10.1215/00294527-2143844


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.


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Jonathan Kirby. "A Note on the Axioms for Zilber’s Pseudo-Exponential Fields." Notre Dame J. Formal Logic 54 (3-4) 509 - 520, 2013.


Published: 2013
First available in Project Euclid: 9 August 2013

zbMATH: 1345.03070
MathSciNet: MR3091668
Digital Object Identifier: 10.1215/00294527-2143844

Primary: 03C65
Secondary: 03C48

Keywords: abstract elementary class , exponential fields , first-order theory , pseudo-exponentiation , Schanuel property

Rights: Copyright © 2013 University of Notre Dame


Vol.54 • No. 3-4 • 2013
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