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Henson and Rubel's theorem for Zilber's pseudoexponentiation

Published online by Cambridge University Press:  12 March 2014

Ahuva C. Shkop
Ahuva C. Shkop*
Affiliation:
Department of Mathematics, Ben Gurion University of the Negev, P.O.B. 653, Be'er Sheva 84105, Israel, E-mail: shkopa@math.bgu.ac.il
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 2 , June 2012 , pp. 423 - 432
Copyright
Copyright © Association for Symbolic Logic 2012

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References

REFERENCES

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