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identity theorem

Journal of the Institute of Mathematics of Jussieu (1)

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COMPARING $\mathbb{C}$ AND ZILBER’S EXPONENTIAL FIELDS: ZERO SETS OF EXPONENTIAL POLYNOMIALS
Part of
- Model theory
- Number theory: Connections with logic
P. D’Aquino, A. Macintyre, G. Terzo
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 15 / Issue 1 / January 2016

Published online by Cambridge University Press:

04 August 2014, pp. 71-84

Print publication:

January 2016
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We continue the research programme of comparing the complex exponential with Zilberś exponential. For the latter, we prove, using diophantine geometry, various properties about zero sets of exponential functions, proved for $\mathbb{C}$ using analytic function theory, for example, the Identity Theorem.