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June 2012 Henson and Rubel's theorem for Zilber's pseudoexponentiation
Ahuva C. Shkop
J. Symbolic Logic 77(2): 423-432 (June 2012). DOI: 10.2178/jsl/1333566630

Abstract

In 1984, Henson and Rubel [2] proved the following theorem: If p(x₁,…,xn) is an exponential polynomial with coefficients in ℂ with no zeroes in ℂ, then p(x₁,…,xn)= eg(x₁,…,xn) where g(x₁,…,xn) is some exponential polynomial over ℂ. In this paper, I will prove the analog of this theorem for Zilber's Pseudoexponential fields directly from the axioms. Furthermore, this proof relies only on the existential closedness axiom without any reference to Schanuel's conjecture.

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Ahuva C. Shkop. "Henson and Rubel's theorem for Zilber's pseudoexponentiation." J. Symbolic Logic 77 (2) 423 - 432, June 2012. https://doi.org/10.2178/jsl/1333566630

Information

Published: June 2012
First available in Project Euclid: 4 April 2012

zbMATH: 1254.03076
MathSciNet: MR2963014
Digital Object Identifier: 10.2178/jsl/1333566630

Rights: Copyright © 2012 Association for Symbolic Logic

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Vol.77 • No. 2 • June 2012
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